# Questions on Algebra: Negative and Fractional exponents answered by real tutors!

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Question 994459: 8 to third power over 8 to the 7 power equals

Question 994458: 8 to the third power over 8 to the seventh power equals
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8 to the third power over 8 to the seventh power equals 0.000244140625

Question 994242: What is -14 to the zero power?
Found 2 solutions by MathTherapy, Alan3354:
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What is -14 to the zero power?
Any expression (number included) to the zero (0) power, with the EXCEPTION of zero (0) equals 1, OR



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1
==========
Anything to the zero power = 1, including zero.

Question 993945: How can you use 2 3 4 and - x ➗ to get the answer -6

Question 993483: How do I simplify (5-1) to the power of 2 minus (6-5) to the power of 3? :)
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Do the arithmetic indicated inside of the parentheses. Raise the resulting quantities to the indicated powers, and then sum the two terms.

John

My calculator said it, I believe it, that settles it

Question 992978: Simplify (x^6)^-2

Question 992818: How do I solve -64 2/3
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It's not an equation, so there's nothing to solve.

Question 992519: how do you rewrite x^6 times y^2 times x^4 using each base only once

Question 992361: Solve this equation!
(x-3)^3/2 = 8

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.
You want to say

Solve this equation,  please!".  Isn't ??

(x-3)^3/2 = 8.
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= .

Square both sides.  You will get

= .

Now take the cubic root from both sides.  You will get

x - 3 = = 4.

The solution is  x = 7.

Question 991769: X+4=3/4

Question 991477: simplify 5 exponent -2 divided by 4 exponent 6
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5^-2 / 4^6 = (1/5^2) / (4^6) = (1/5^2) * (1/4^6) = 1 / (5^2 * 4^6).

i believe that's as simple as it gets without actually evaluating 5^2 = 25 and 4^2 = 4096 and then multiplying 25 * 4096 to get 1/102400.

Question 991464: 2a+6=27
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Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

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So the solution is (as a decimal, the answer is )

Question 991375: Write 0.6 in exponent form
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Write 0.6 in exponent form
----
Do you mean scientific notation?
= or 6e-1
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=

Multiply and simplify completely, including the elimination of all negative exponents:
(3x^5)/(4y^10) (4^4y^7)/(3^3X^9)
Enter your answers for the numerator and denominator separately in the boxes below.

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It's not clear what in the NUM and DEN.

Question 990844: 4x raised to the power negative 2/(divided) by (4) raised to the power negative 2
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Enter it in math terms.

Question 990285: 1/243

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Do you have a question?

Question 990188: 3/4x-2/3y=2
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.
Very good.

And what do you want?

Question 989279: 19/12=-7/2b+1/3b

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19/12=-7/2b+1/3b
19/12=-21/6b+2/6b
19/12=-19/6b
(19/12)/(-19/6)=b
[b=-1/2]
-Aμstin

Question 988479: use two unit multipliers to convert 10000 inches to miles

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[ inches ] x [ ft/in ] x [ mi/ft ]

miles

Question 987016: What is 81;base 9?

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What is 81;base 9?
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100

Question 986978: It has been a long time since I've done this and need to help my son with his homework. Could you please work this problem out step by step, so that I can make sure I'm doing this correctly??? I would really appreciate it. Thankyou!!!
SOLVE:
2/3X = -12
MY EMAIL IS sgauthier1202@gmail.com

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.

Multiply each side by 3.
Divide each side by 2.

Question 986805: How do you solve 451-(3*2)exponent 4
Ive tried the two ways i know but it keeps telling me Na
Help

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451-(6)^4=
451-(1296)=-845

Question 986628: What is -5/3 as a whole number?
Needing to find out the whole number for negative five thirds?

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-5/3 is not a whole number.
It's a fraction.

Question 985892: Okay so I'm trying to figure out how to evaluate this expression. 9^-3 • 9^5 over 9^-2 all to the negative half power.
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9^-3*9^5=9^2.
9^2/9^(-2)=9^4
(9^4)^(-1/2)=9^(-2)
=(1/81)

Question 985797: -5/9X=-45
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.
-5/9X=-45 Multiply by -9/5
X=(-9/5)(-45)
X=(-9)(-9)
x=81

Question 984972: square root of (y2 - x)
or
1/2 power of (y2 - x)

Found 2 solutions by Alan3354, Boreal:
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Do you have a question?

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They are both equivalent, although I would say (y^2-x) to the (1/2) power.

Question 984832: Express in the form where p and q are rational numbers.
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Say this better as 2+4*sqrt(6)/(3*sqrt(2))-3
rendered as .

, and not much more that can be done with the rational integer, ; you could put it as this for final requested form of the result:

Question 984834: Solve the following equation: Sqrt14-x=sqrtx-4+sqrtx-1

Question 984838: Find the 35th term of an A.P whose first term is 6 and common difference is 3/2
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Hi dear,
using the formula

substitute the above in the formula

=6+102/2
=6+51
= 57
The 35th term is 57.
HOPE THIS HELPS;
TIMNEWMAN::

Question 984657: What number is halfway between -5 and 7?
Found 2 solutions by MathLover1, Alan3354:
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to find a number is halfway between and , first find the distance between and is
divide the distance by :
subtract from :
so, a number halfway between and is

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What number is halfway between -5 and 7?
==============
The average
= (-5 + 7)/2
= 1

Question 984583: I need to simplify
(10vy^5+2v^4)/(2v^2w^3)

Question 983653: How do I solve(fraction ) 1/-3x to the power of -2
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Equations are solved.
eg, you'll see, "Solve for x."
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Fractions are not solved.

Question 982696: quantitative comparison
t is an integer
COl A: 1/1+2^t

COL B: 1/1+3^t

Is it correct to say you cannot determine which is larger without additional information.
My reasoning is if t is positive, the col a is larger. and if t is negative, the col b is larger.
Is this correct? Am I missing anything? Please explain. Thanks! :)

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is larger than when

So is larger than when

Ultimately, is smaller than when . The reciprocals make the relationship swap.
Eg: 6 > 5 so 1/6 < 1/5 (since 0.167 < 0.2)

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Note: if , then everything flips. So if they say "t is an integer" then there isn't enough info. If they said "t is a POSITIVE integer" then that's enough info to figure out that col A is larger.

Question 981274: please solve x in the equation , x^2-x-12 equals 0
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...to factor completely write as
....group

solutions:
if =>}
if =>
see it on a graph

Question 981053: Hi appreciated math tutors.
I am not sure how to solve the following problem, it reads:
A piece of notebook paper is about .0032 inch thick. If you begin with a stack consisting of a single sheet and double the stack 25 times, how tall will the stack be in inches? HINT: Write and solve an exponential equation to find the height of the stack in inches.
I tried to solve the problem by multiplying .0032 by two and raising this product to the 25th power, but it comes out to be a very small negative number. Of curse, a negative answer is not correct. Please demonstrate how to solve and if an inverse is taken, please explain why if possible. Thank you!

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A piece of notebook paper is about .0032 inch thick. If you begin with a stack consisting of a single sheet and double the stack 25 times, how tall will the stack be in inches? HINT: Write and solve an exponential equation to find the height of the stack in inches.
I tried to solve the problem by multiplying .0032 by two and raising this product to the 25th power, but it comes out to be a very small negative number.
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If you fold it once, it's 0.0064 thick.
Twice, it's 0.0128 thick, etc
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Height = 0.0032*2^25
= 0.0032*33554432 inches
= 107374.1824 inches
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=~ 1.695 miles

Question 978959: What is the square root of 1446
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=> decimal approximation

Question 977404: 8x^2 /x^-2 y^2 * (4xy^2)^-1 /x^2 y

Question 977398: Simplify (-3x^-2 y^0)^-3
no negative exponents allowed in final answer.
Please help with this question and explain it thoroughly because i have to do lots of problems like this and I need a bit of briefing before I do them. Thank you :)
PS: y is separated from the 2

Found 2 solutions by rothauserc, Fombitz:
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(-3x^-2 y^0)^-3 =
(-3x^-2)^-3
note that y^0 = 1
(-3x^-2)^-3 =
-3^-3 *x^6
multiply exponents inside parenthesis by -3
-3^-3 *x^6 =
-x^6 / 3^3 =
-x^6 / 27

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(-3x^(-2)y^(0))^(-3)
Use parentheses to separate the exponents.
This way it's clear and you don't need to explain.

Question 975824: Add -2/5 + 7/12
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Find a common denominator.
The product always works.
5*12 = 60
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-2/5 + 7/12 = -24/60 + 35/60
= 11/60

Question 975371: help me please:) i can't get the right answer for this rational exponent...

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As written above, it is the numerator with no exponent (1 is implied) over 5.
If it is raised to the one-fifth power, then you multiply the exponents.
32 * n* p^2
example (32^5)^(1/5)=32^1 or 32.
(p^10)^(1/5)=p^2.

Question 975368: .i truly need help,will someone please solve this for me:)
x to the power of negative one half times the exponent of negative two.