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Tutors Answer Your Questions about Exponents-negative-and-fractional (FREE)
Question 175089: is there somewhere on the internet where it could help me solve the question?
Here is one of the questions it says Remove the radical from the denominator of the following fraction without changing the value of the fraction. could you please explain this to me step by step and show me this method with an example?
: is there somewhere on the internet where it could help me solve the question?
Here is one of the questions it says Remove the radical from the denominator of the following fraction without changing the value of the fraction. could you please explain this to me step by step and show me this method with an example?
Answer by solver91311(2177)  (Show Source):
You can put this solution on YOUR website!You are describing a process called "Rationalizing The Denominator" which simply means to convert the fraction so that the denominator is a rational number. The trick is to multiply the fraction by 1 in the form of  where  is selected so that after the multiplication the denominator is a rational number.
For example, rationalize the denominator of  . In order for the denominator to be rational, we need to multiply it by  , so that is our value for in this case. The process looks like this:
The process becomes a little more complex when you are faced with a denominator that is in the form  where either or  (or both, for that matter) is irrational. In this situation, say if we had  as a denominator, there is no simple number that we can use as a multiplier to convert this denominator to a rational number.
What you need to do is to recall the "difference of two squares" factorization, namely:  . That means you can take something like and multiply by it's conjugate,  to arrive at 
Let's do an example:
Rationalize: 
The conjugate of the denominator is  , so we have to multiply the original fraction by 1 in the form of  , thus:
You can read more about this at:
http://www.math.unt.edu/mathlab/emathlab/How%20to%20Rationalize%20the%20Denominator%20of%20a%20Fraction.htm
http://www.helpalgebra.com/articles/rationalizedenominator.htm
Or just Google "rationalize the denominator" for a bunch more.
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Question 175019: how do i simplify the expression 6*the sqroot of 2 over square root of 3?: how do i simplify the expression 6*the sqroot of 2 over square root of 3?
Answer by Mathtut(1309) (Show Source): |
Question 174957: how do i find the value of x in the equation x/2+20=15+x/3?: how do i find the value of x in the equation x/2+20=15+x/3?
Answer by Electrified_Levi(95) (Show Source):
You can put this solution on YOUR website!Hi, Hope I can help,
.
how do i find the value of x in the equation  ?
.
First of all, we have to get rid of the fractions
.
We have to find a common denominator with the fractions
.
The first fraction,  , has "2" as its denominator
.
The second fraction,  , has "3" as its denominator
.
To find the common denominator, we would just multiply the two denominators together ( since there is no lower denominator we could use )
.
 = 
.
"6" is the common denominator, now if we multiply the two sides of the equation, it will get rid of the fractions, since they both will cancel out
.
= 
.
We can now use the distributive property,
.
 =  = 
.
=  , now we will simplify even further by dividing
.
=  =  =  = 
.
Now all we do is solve for "x", we will move "2x" to the left side
.
=  =  , now we will move "120" to the right side
.
=  = 
.
.
You can check by replacing "x" with (-30) in the very original equation
.
replace "x" with (-30), =  =  =  =  ( True )
.
You have to be careful with fraction equations, because the denominator of a fraction cannot equal 0, so if one of the answers make a denominator 0, then that answer cannot work
.
We don't have anything to worry about, since there are no "x"'s in the denominator
.
.
Hope I helped, Levi
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Question 174957: how do i find the value of x in the equation x/2+20=15+x/3?: how do i find the value of x in the equation x/2+20=15+x/3?
Answer by stanbon(19692) (Show Source):
You can put this solution on YOUR website!find the value of x in the equation x/2+20=15+x/3?
-----------------
x/2 - x/3 = -5
(3x-2x)/6 = -5
x = -30
==================
Cheers,
Stan H.
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Question 174957: how do i find the value of x in the equation x/2+20=15+x/3?: how do i find the value of x in the equation x/2+20=15+x/3?
Answer by Mathtut(1309) (Show Source): |
Question 174956: How do i simplify the expression (6x^3 over 3x^4)^2?: How do i simplify the expression (6x^3 over 3x^4)^2?
Answer by Mathtut(1309) (Show Source): |
Question 174959: How do I simplify the expression 2 divided by 6 over 3divided by 0 ?: How do I simplify the expression 2 divided by 6 over 3divided by 0 ?
Answer by Mathtut(1309) (Show Source): |
Question 174960: how do I find the square root of the fraction 64 over 100?: how do I find the square root of the fraction 64 over 100?
Answer by Mathtut(1309) (Show Source):
You can put this solution on YOUR website!you can either do it by calulator or knowing that the square root of 64 is 8 and the square root of 100 is 10 meaning your left with the fraction
:
8/10=4/5 so  =4/5
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Question 174963: What is the lenth of a leg if of a right triangle if one leg is 15 centimeters and the hypotenuse is 20 inches?: What is the lenth of a leg if of a right triangle if one leg is 15 centimeters and the hypotenuse is 20 inches?
Answer by stanbon(19692) (Show Source):
You can put this solution on YOUR website!What is the length of a leg if of a right triangle if one leg is 15 centimeters and the hypotenuse is 20 inches?
-----------------
20^2 = L^2 + 15^2
400 = L^2 + 225
L^2 = 175
L = 5sqrt(3) cm
=====================
Cheers,
Stan H.
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Question 174962: How do I find the hypotenuse of a right triangle with one leg at 3 centimeters and the other leg measure 6 centimeters?: How do I find the hypotenuse of a right triangle with one leg at 3 centimeters and the other leg measure 6 centimeters?
Answer by stanbon(19692) (Show Source):
You can put this solution on YOUR website!find the hypotenuse of a right triangle with one leg at 3 centimeters and the other leg measure 6 centimeters?
-----------------------
Use Pythagoras to get:
h = sqrt[3^2 + 6^2]
= sqrt[45]
= 3sqrt(5) cm.
================
Chers,
Stan H.
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Question 174958: how do I simplify the expression r^-3s^5t^2 over r^2st^-2?: how do I simplify the expression r^-3s^5t^2 over r^2st^-2?
Answer by stanbon(19692) (Show Source):
You can put this solution on YOUR website!simplify the expression r^-3s^5t^2 over r^2st^-2
--------
= [s^4t^4] / [r^5]
===================================
Cheers,
Stan H.
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Question 174878: I need help to simplify r^-3s^5t^2 over r^2st^-2?: I need help to simplify r^-3s^5t^2 over r^2st^-2?
Answer by Alan3354(1926) (Show Source): |
Question 174878: I need help to simplify r^-3s^5t^2 over r^2st^-2?: I need help to simplify r^-3s^5t^2 over r^2st^-2?
Answer by stanbon(19692) (Show Source):
You can put this solution on YOUR website!I need help to simplify r^-3s^5t^2 over r^2st^-2?
(r^-3s^5t^2) / (r^2st^-2)
= (s^4t^4) / (r^5)
===========================
Cheers,
Stan H.
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Question 174875: how do I simplify (6x^3 over 3x^4)^2?: how do I simplify (6x^3 over 3x^4)^2?
Answer by checkley75(3410) (Show Source): |
Question 174803: How do i reduce the fraction -20t^5u^2v^3 over 48t^7u^4v?: How do i reduce the fraction -20t^5u^2v^3 over 48t^7u^4v?
Answer by Alan3354(1926) (Show Source): |
Question 174780: Make sure to supersript all exponents in the final answers should be positive. Final answers should have all single connecting signs and be arranged in descending order.
For f(x)=3x-5,find f(2)
Thanks ;): Make sure to supersript all exponents in the final answers should be positive. Final answers should have all single connecting signs and be arranged in descending order.
For f(x)=3x-5,find f(2)
Thanks ;)
Answer by Alan3354(1926) (Show Source): |
Question 174758: Thanks for all your help!!
1) Simplify and evaluate:
(x^3y^-4z^0/3x^6y^-3)^4
3)Convert to scientific notation:
0.003816: Thanks for all your help!!
1) Simplify and evaluate:
(x^3y^-4z^0/3x^6y^-3)^4
3)Convert to scientific notation:
0.003816
Answer by ankor@dixie-net.com(4667) (Show Source):
You can put this solution on YOUR website!1) Simplify and evaluate:
z^0 = 1 so we can write it:
Combine like term exponents in a manner that will make the results positive:
 = 
3)Convert to scientific notation:
0.003816
:
Move the decimal 3 places to the right and you have: 3.816(10^-3)
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Question 174764: Make sure to supersript all exponents in the final answers should be positive. Final answers should have all single connecting signs and be arranged in descending order.
1) For f(x)=3x-5,find(2).
2)Multiply
(4x+1)(2x^2+5x+1): Make sure to supersript all exponents in the final answers should be positive. Final answers should have all single connecting signs and be arranged in descending order.
1) For f(x)=3x-5,find(2).
2)Multiply
(4x+1)(2x^2+5x+1)
Answer by Mathtut(1309) (Show Source): |
Question 174749: Would someone please help me with this I'm just not getting it. Thank you!!
Make sure to supersript all exponents in the final answers should be positive. Final answers should have all single connecting signs and be arranged in descending order.
A) Perform the indicated operations:
(5x^2-3x+2)+(-3x^2+9x-8)-(x^2+3x-10)
B) Use FOIL to multiply:
(3x-8)(x-7): Would someone please help me with this I'm just not getting it. Thank you!!
Make sure to supersript all exponents in the final answers should be positive. Final answers should have all single connecting signs and be arranged in descending order.
A) Perform the indicated operations:
(5x^2-3x+2)+(-3x^2+9x-8)-(x^2+3x-10)
B) Use FOIL to multiply:
(3x-8)(x-7)
Answer by stanbon(19692) (Show Source):
You can put this solution on YOUR website!A) Perform the indicated operations:
(5x^2-3x+2)+(-3x^2+9x-8)-(x^2+3x-10)
= (5x^2-3x^2-x^2)+(-3x+9x-3x)+(2-8+10)
= x^2 + 3x +4
===============================
B) Use FOIL to multiply:
(3x-8)(x-7)
F: 3x*x = 3x^2
O:3x*-7 = -21x
I:-8*x = -8x
L: -8*-7 = 56
------------------
Combine the terms to get:
= 3x^2 -29x + 56
========================
Cheers,
Stan H.
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Question 174666This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: (12) The number of electric blankets sold at Jenkin's Home Furnishings from January 1 through December 31 can be represented by the function y= 680cos(pie/6 t) + 708 in which t is time in months with t =0 corresponding to january 1. Determine when the fewest electric blankets were sold and how many were sold.
Show work thanksThis question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: (12) The number of electric blankets sold at Jenkin's Home Furnishings from January 1 through December 31 can be represented by the function y= 680cos(pie/6 t) + 708 in which t is time in months with t =0 corresponding to january 1. Determine when the fewest electric blankets were sold and how many were sold.
Show work thanks
Answer by stanbon(19692) (Show Source):
You can put this solution on YOUR website!The number of electric blankets sold at Jenkin's Home Furnishings from January 1 through December 31 can be represented by the function y= 680cos(pie/6 t) + 708 in which t is time in months with t =0 corresponding to january 1. Determine when the fewest electric blankets were sold and how many were sold.
------------------------------------------------
y = 680cos((pi/6)t) + 708
----------------------------
The minimum value of cos occurs when the angle is pi radians.
----------------------------
Equation:
(pi/6)t = pi
t = 6 (time at which the cosine has its minimum value)
----------------
f(6) = 680cos[pi] + 708 = 680*-1 + 708 = 28
===================
Cheers,
Stan H.
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Question 174628This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: 6) If 4^x = 2^y and 9^x-1 = 3^x+1, which of the following are the values of x and y?
(a) x = 2, y = 4 (b) x=3, y=6 (c) x=4, y=2 (d) x=6, y=3
7)When David was born, his grandparents deposited $1,000 in a college account that promised 4 percent interest compounded annually for 18 years. Which of the following equations shows the worth of the account when David is 18?
(a) y = 18(4)($1,000)
(b) y = 18(0.04)($1,000)
(c) y = $1,000(0.04)^18
(d) y = $1,000(1.04)^18
Show work thanks so much!This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: 6) If 4^x = 2^y and 9^x-1 = 3^x+1, which of the following are the values of x and y?
(a) x = 2, y = 4 (b) x=3, y=6 (c) x=4, y=2 (d) x=6, y=3
7)When David was born, his grandparents deposited $1,000 in a college account that promised 4 percent interest compounded annually for 18 years. Which of the following equations shows the worth of the account when David is 18?
(a) y = 18(4)($1,000)
(b) y = 18(0.04)($1,000)
(c) y = $1,000(0.04)^18
(d) y = $1,000(1.04)^18
Show work thanks so much!
Answer by ankor@dixie-net.com(4667) (Show Source):
You can put this solution on YOUR website!6) If 4^x = 2^y and 9^x-1 = 3^x+1, which of the following are the values of x and y?
:
In the 1st equation, we can write 4^x as 2^(2x), so we have
2^(2x) = 2^y
Therefore:
2x = y
:
In the 2nd equation, the same:
3^(2(x-1)) = 3^(x+1)
therefore
2(x-1) = x + 1
2x - 2 = x + 1
2x - x = 1 + 2
x = 3
2x = y, therefore
y = 6
:
:
7)When David was born, his grandparents deposited $1,000 in a college account that promised 4 percent interest compounded annually for 18 years. Which of the following equations shows the worth of the account when David is 18?
:
The interest is added to the accumulated amt each year for 18 yrs, therefore:
(d) 1000*(1.04)^18
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Question 174166: (5a-b)/(5a+b)
can you show the steps to simplify this equation?
Thank you: (5a-b)/(5a+b)
can you show the steps to simplify this equation?
Thank you
Answer by Edwin McCravy(2190) (Show Source):
You can put this solution on YOUR website!(5a-b)/(5a+b)
can you show the steps to simplify this equation?
First of all it is not an equation, but an expression.
Equations always have equal signs.
There is no way to simplify it. It could possibly
be divided by long division:
1
-------
5a + b)5a - b
5a + b
------
-2b
and thus  but that's not exactly
simplifying.
Edwin
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Question 173468: I need help with simplifing this equation can you help?
(2^1/2x^3/5y^-7/5/z^1/10)^-10: I need help with simplifing this equation can you help?
(2^1/2x^3/5y^-7/5/z^1/10)^-10
Answer by bob123132(20) (Show Source):
You can put this solution on YOUR website!Well i dont know if i am mixing up this up at all because you kinda flunked out on putting in the brackets on each term,but this is how i interpreted it. all you have to do is multiply each exponent by -10
ex.  or 
So if you work it out you should get:
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Question 173464: Could you please check my answer to this equation it needed to be simplified.
16^1/4-(-32)^1/5 my answer was 2-32^1/5: Could you please check my answer to this equation it needed to be simplified.
16^1/4-(-32)^1/5 my answer was 2-32^1/5
Answer by solver91311(2177) (Show Source):
You can put this solution on YOUR website!You are only half done. Hint:  Furthermore, double check your sign between the two terms, you are about to make a mistake there, too.
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Question 172580: I need some help with simplyfing fractional exponets can you help?
(16^1/4)- (-32)^1/3): I need some help with simplyfing fractional exponets can you help?
(16^1/4)- (-32)^1/3)
Answer by Alan3354(1926) (Show Source):
You can put this solution on YOUR website!(16^1/4)- (-32)^1/3)
-----------
16^(1/4) = 2
----------------
(-32)^(1/3) = -8^(1/3)*(4)^(1/3) = -2*(4^(1/3))
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So (16^1/4)- (-32)^1/3) = 2 + 2*cube root(4)
=~ 2 + 1.5874
=~ 3.5874
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Question 172564: I am having a problem on how to solve these kinds of problems. One example of this is.... (-11)to the -2 power multiplied by Y to the 0 power. can you please help me?!?!?!?!: I am having a problem on how to solve these kinds of problems. One example of this is.... (-11)to the -2 power multiplied by Y to the 0 power. can you please help me?!?!?!?!
Answer by Earlsdon(3816) (Show Source): |
Question 172412: how do you solve this problem 24c to the thirdpower d over 36 c to the second powerd: how do you solve this problem 24c to the thirdpower d over 36 c to the second powerd
Answer by Alan3354(1926) (Show Source):
You can put this solution on YOUR website!how do you solve this problem 24c to the thirdpower d over 36 c to the second powerd
------------
 If that's what you meant.
There's nothing to solve. This is a fraction that can be reduced.
Divide NUM and DEN by 12c^2
= 
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Question 171372This question is from textbook Algebra 1
: Add:
a
- + 5
---- + b
---- =?
d cubed
d
4d squared This question is from textbook Algebra 1
: Add:
a
- + 5
---- + b
---- =?
d cubed
d
4d squared
Answer by Alan3354(1926) (Show Source): |
Question 170497: Choose values of x to show that 2x^2-32/x-4 does not simplify to 2x-8. Then, simplify it correctly.
I simplified it and got that the correct answer is 2x+8. I do not know how to choose values of x to show that 2x-8 is incorrect.
Thank you for any help you can provide.: Choose values of x to show that 2x^2-32/x-4 does not simplify to 2x-8. Then, simplify it correctly.
I simplified it and got that the correct answer is 2x+8. I do not know how to choose values of x to show that 2x-8 is incorrect.
Thank you for any help you can provide.
Answer by stanbon(19692) (Show Source):
You can put this solution on YOUR website!Choose values of x to show that 2x^2-32/x-4 does not simplify to 2x-8.
------
Assume [2x^2-32/x-4] = [2x-8]
Test x = 0
You get [(0-32)/(0-4)] = [0-8]
or [-32/-4] = [-8]
or 8 = -8 , which is wrong.
----------------------------
This shows that the assumed equality is not true.
=======================================
Cheers,
Stan H.
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Question 170391: Name the steps in simplifying fractions.
I have Step 1: factor numerator and denominator
I had Step 2: state restrictions on variable/look for opposites so that denominator does not equal zero.
My answer for step 2 is incorrect. Step 1 is correct: Name the steps in simplifying fractions.
I have Step 1: factor numerator and denominator
I had Step 2: state restrictions on variable/look for opposites so that denominator does not equal zero.
My answer for step 2 is incorrect. Step 1 is correct
Answer by Mathtut(1309) (Show Source): |
Question 167823: Simplify the expression:
(9y^4 x^1/2)^1/2. Please help.: Simplify the expression:
(9y^4 x^1/2)^1/2. Please help.
Answer by checkley77(3848) (Show Source): |
Question 167625: simplify using positive exponents
(x-4)(x+4x+16): simplify using positive exponents
(x-4)(x+4x+16)
Answer by stanbon(19692) (Show Source): |
Question 167626: simplify
(4x^2-4x+3)/(x-2): simplify
(4x^2-4x+3)/(x-2)
Answer by stanbon(19692) (Show Source):
You can put this solution on YOUR website!(4x^2-4x+3)/(x-2)
----------------------------
Using synthetic division:
2)....4....4....3
.......4....12..|..27
=============================
Quotient: 4x^2 + 12
Remainder: 27
=============================
Cheers,
Stan H.
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Question 166997: Determine the root under the set of real numbers.
What is the square root of -16: Determine the root under the set of real numbers.
What is the square root of -16
Answer by checkley77(3848) (Show Source): |
Question 166912: can you please help me solve this problem?
(5x)(10x^2): can you please help me solve this problem?
(5x)(10x^2)
Answer by checkley77(3848) (Show Source): |
Question 164641: Perform indicated operation. Please help me.
(6y^3 - 9y^2)/-3y: Perform indicated operation. Please help me.
(6y^3 - 9y^2)/-3y
Answer by Fombitz(1782) (Show Source): |
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