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

Tutors Answer Your Questions about Exponents-negative-and-fractional (FREE)

Question 571525: please simplify below
M2+4M-32
_________
mq+8q

Answer by reviewermath(39)

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Factor the numerator and denominator, then cancel the common factors
%28m%5E2%2B4m-32%29%2F%28mq%2B8q%29+=+%28m%2B8%29%28m-4%29%2Fq%28m%2B8%29

%28m%5E2%2B4m-32%29%2F%28mq%2B8q%29+=+%28m%2B8%29%28m-4%29%2Fq%28m%2B8%29

cross%28%28m%2B8%29%29%28m-4%29%2Fq%28cross%28m%2B8%29%29

Answer:

Question 571040: How do you simplify a product ex: 2y(y + 1)
Answer by nyc_function(2645)

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2y(y + 1) =

Multiply every term inside the parentheses with the outside term 2y.

2y times y = 2y^2

2y times 1 = 2y

Final answer = 2y^2 + 2y

Question 570427: I am having trouble with this question:
7^sqrt(a^2*b^4)
So far I have come up with this:
ab^2/7, a^2/7*b^4/7 = (ab)^8/7, (a^2)^1/7(b^4)^1/7.
If you could help with this question, it would be much appreciated.
Thank You.
Answer by Alan3354(21608)

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7%5Esqrt%28a%5E2%2Ab%5E4%29

Question 569875: c15/c9

Answer by jim_thompson5910(21685)

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(c^15)/(c^9) = c^(15-9) = c^6

So (c^15)/(c^9) = c^6

Question 569784: (.04) To the third power?
Answer by Alan3354(21608)

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(.04) To the third power?
0.04%5E3+=+%284%2A10%5E-2%29%5E3+=+64%2A10%5E-6

64E-6 = 0.0000064

Question 569669: Find the equivalent expression to 2^-5
Answer by Alan3354(21608)

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Find the equivalent expression to 2^-5
--------
2%5E-5+=+1%2F%282%5E5%29+=+1%2F32

Question 569380: Please show me the steps to simply this;
4c^-1m^2/s^-3
Thank you
Answer by ankor@dixie-net.com(12704)

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%284c%5E-1m%5E2%29%2Fs%5E-3+

Remember the reciprocal of the terms gets rid of the neg exponent
%284m%5E2%29%2F%28c%5E1s%5E-3%29+

and

: (c^1 is just c)

Question 568938: How to calculate -10 ^ 0.5
-10 Power 0.5
Answer by Theo(2978)

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(-10) ^ .5 is the same as:
(-10) ^ (1/2) which is the same as:
sqrt (-10) which is not a real number.

- (10)^.5 is the same as:
- (10)^(1/2) which is the same as:
- sqrt(10) which you can solve using the square root function of your calculator.

the answer becomes 3.16227766.

you confirm this is the answer by squaring it to get back to 10.

Question 568190: How to solve without a calculator? (x^-4/5)^-5/6
Found 2 solutions by Edwin McCravy, mananth:
Answer by Edwin McCravy(6939)   (Show Source):
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To remove the parentheses, multiply the exponents = = = = Edwin

Answer by mananth(10554)   (Show Source):
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use the law

x^(2/3)

Question 564975: evaluate without using a calculator
(-243)^1/5
Answer by Alan3354(21608)   (Show Source):
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(-243)^1/5 = -3
------------------
You can do it without a calculator if you know that.
If you don't know it, then you have to poke around and find it.

Question 564973: evaluate without using a calculator
(-243)6^1/5
Answer by Alan3354(21608)   (Show Source):
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evaluate without using a calculator
(-243)6^1/5
------------
What does the 6 mean?
-243 = (-3)^5

Question 564141: write z^4/z^-6 in simplest form with positive exponents
Answer by mananth(10554)   (Show Source):
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Question 563861: Please help me solve this equation: 1-25y^-2/1+10y^-1+25y^-2
Answer by mananth(10554)   (Show Source):
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Question 562447: How do I simplify (6.5x10^8)^-4? Plz show steps so I understand.
Krambeers4@sbcglobal.net
Answer by Alan3354(21608)   (Show Source):
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How do I simplify (6.5x10^8)^-4?
---------
=
=
=
Is that simpler?
Or
Or 5.602E-36 ?
-----
Simplified can be a matter of opinion.

Question 561764: can you help me with this please : 5-(-2)+(-3)+2/(-1)-1
Answer by ankor@dixie-net.com(12704)   (Show Source):
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5-(-2)+(-3)+2/(-1)-1
the problem of this is:
is it:

or
5-(-2)+(-3)+-1
or
5-(-2)+(-3)+

Question 561001: What are the prime factors of 1,350 using exponential notations
Answer by stanbon(48568)   (Show Source):
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prime factors of 1,350 using exponential notations
---
1350 = 50*27
---
= 2*5^2*3^3
==================
Cheers,
Stan H.
=======================

Question 560584: 1. 17 degrees 49 minutes and 10 seconds added to 22 degrees 22 minutes and 59 seconds, equals to?
2. To what power must 10 be raised to equal 100,000?
3.Area of a right circular cone of base radius r, and height l, is
4.The supplement of 13 degrees is
5.64y = 64

Answer by Edwin McCravy(6939)   (Show Source):
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1. 17 degrees 49 minutes and 10 seconds added to 22 degrees 22 minutes and 59 seconds, equals to?

17° 49' 10" +22° 22' 59" 39° 71' 69" Subtract 60" from 69" and get 9". Add 1' to the 71' and get 72'. So now you have: 39° 72' 9" Next subtract 60' from 72' and get 12'. Add 1° to the 39° and get 40°. So you end up with 40° 12' 9"

2. To what power must 10 be raised to equal 100,000?

Count the zeros in 100,000. There are 5 of them. Therefore 10⁵ = 100,000. Answer: the fifth power.

3. Area of a right circular cone of base radius r, and height l, is

A cone has two dimensions that are both called "heigths". Ususlly l is for the lateral height, and h for the actual height. So I'm not sure what you mean, since you just said "height" but used l. The lateral surface area of a right circular cone is where is the radius of the circle at the bottom of the cone and is the lateral height of the cone (given by the Pythagorean theorem where is the actual height of the cone). The surface area of the bottom circle of a cone is the same as for any circle, . Thus the total surface area of a right circular cone is: or 4.The supplement of 13 degrees is 180° - 13° = 167°

5. 64y = 64

Divide both sides by 64 = Cancel the 64's onthe left and divide on the right: = or y = 1 Edwin

Question 559989: help: x^1/7*y^1/6*z^1/3
Answer by Alan3354(21608)   (Show Source):
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help: x^1/7*y^1/6*z^1/3
-----------
Help what? What do you want to do?

Question 558782: I don't understand how to solve a fraction to a negative (whole number) exponent. Can you please explain it to me?

Found 2 solutions by rapaljer, stanbon:
Answer by rapaljer(4551)   (Show Source):
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A fraction raised to a negative exponent, essentially means to INVERT the fraction. means

means invert the fraction and square, like this which is 25/9.

For a complete explanation of negative exponents with LOTS of examples and exercises, please see my website. To go to my website, use the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. At the very bottom of this page, there is a link that will take you to my Homepage.

Once you are on my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in "Chapter 2," for "Section 2.13 Laws of Exponents: Negative and Zero" for a complete, non-traditional explanation that my own students, before I retired, found a lot easier to understand than the published textbooks of that day. You should really like my MATH IN LIVING COLOR pages, where the most difficult problems are solved IN COLOR. In addition, I have a video of me teaching this topic before I retired.

Everything on the website is FREE. If you find something you really like, just print your own copy of it!!

If anyone needs to contact me, especially about the website, my Email address is rapaljer@seminolestate.edu. I'll be glad to help you find an explanation on my website to help you with your algebra topic!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

Answer by stanbon(48568)   (Show Source):
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I don't understand how to solve a fraction to a negative (whole number) exponent. Can you please explain it to me?
------
The "negative" in an exponent means "invert".
----
Examples:
3^-2 = 1/(3^2) = 1/9
------------------------
16^(-3/2)
The 2 means take the square root.
The 3 means cube
The negative means invert
-----
You may perform these directions in ANY order:
Taking the square root you get:
4^(-3)
---
Inverting you get: (1/4)^3
----
Cubing you get: 1/64
===========================
Cheers,
stan H.
=====================

Question 558330: please help me to solve this problem: (-15y^2z) (-2y^2z^0) im confused, i don't know if i have to multiply or divide
Answer by JBarnum(1826)   (Show Source):
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first off its multiplication and z^0=1 since 1 is being multiplied and not added it isnt even needed and can be erased from problem because 1 times y = y

multiplying 2 negatives makes a possitive, and then need to add the like exponents

Question 557339: Write an equivalent expression using negative exponents 6 over y to the third power
Answer by Theo(2978)   (Show Source):
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6/y^3 is the same as 6*y^(-3)
in general:
x^(-a) = 1 / x^a
1 / x^(-1) = x^a
the variable becomes it's reciprocal and the exponent changes it's sign.
some examples:
5^2 = 25
5^(-2) = 1/25
1/5^2 = 1/25
1/5^(-2) = 25
you can use your calculator to confirm.

Question 557120: Simplify the following expression, and rewrite it in an equivalent form with positive exponents.
(4x^-3)^-4

Answer by stanbon(48568)   (Show Source):
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Simplify the following expression, and rewrite it in an equivalent form with positive exponents.
(4x^-3)^-4
----
= (1/4)^4(x^12)
---
= (1/256)x^12
=================
Cheers,
Stan H.

Question 555712: Evaluate (16/25)^(-4/2) to an exact value.
I have no idea where to even start with this problem, please help me! Thank you
Answer by Alan3354(21608)   (Show Source):
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Evaluate (16/25)^(-4/2) to an exact value.
I have no idea where to even start with this problem,
---------------
Start with the exponent, -4/2 = -2.

Question 555717: what is 8 to the -2nd power in simplest form?
Answer by jim_thompson5910(21685)   (Show Source):
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So

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Question 555490: Please help me solve this equation: 2xy^4/5xy^2 x -30xy/2x^2y

Answer by edjones(7311)   (Show Source):
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2xy^4/5xy^2 x -30xy/2x^(2)y
=2y^2/5 - 15/x
=(2xy^2-75)/5x
.
Ed

Question 555453: How do you figure out (x^3)^4
Found 2 solutions by Hankmanscott, jim_thompson5910:
Answer by Hankmanscott(3)   (Show Source):
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X^12

Answer by jim_thompson5910(21685)   (Show Source):
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So

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Question 555441: How do to solve 6^ -2 as a fraction?
Answer by jim_thompson5910(21685)   (Show Source):
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So

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Question 554674: I am trying to understand a problem, 6(3rd power) multiplyed by 6(negative 2 power), which i get 6 by adding the exponents (3+-2) and get 1, so 6x1=6, but then I try to find it a way my math book tells me to, and i do 6x6x6 and get 216, then do the same for the other and i get -36. But 216x-36 DOES NOT EQUAL 6! what am i doing wrong?
Answer by jim_thompson5910(21685)   (Show Source):
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6^(-2) = 1/(6^2) = 1/36

NOT

6^(-2) = -36 <<<--- This is INCORRECT

Question 554492: hi there , how do i express 3 to the power of negative 2 as a fraction?
Answer by Theo(2978)   (Show Source):
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3^(-2) = 1/(3^2) = 1/9

Question 554403: Please tell me how to make this problem into a fraction. the problem is -5 to the -3rd power . I have the givin answers on my paper to choose from and they are 1/125 , -1/125 , 1/15 , -1/15 . I do not understand how to work this problem.
Answer by Maths68(1166)   (Show Source):
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=
=
=
=
=

Question 553816: #49
express using a positve exponent
u^-9
Answer by jim_thompson5910(21685)   (Show Source):
You can put this solution on YOUR website!

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Question 553433: Please help me solve this equation related to solving systems using substitution:
x=y
x+2y=3
Answer by mananth(10554)   (Show Source):
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x=y
x+2y=3
substitute x as y
y+2y=3
3y=3
y=1

x=1

Question 553118: How do I write 8^-9 as a positive exponent?
Found 2 solutions by jim_thompson5910, nerdybill:
Answer by jim_thompson5910(21685)   (Show Source):
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Answer by nerdybill(5412)   (Show Source):
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How do I write 8^-9 as a positive exponent?
By moving the term to the denominator:

would be equivalent to:

Question 552863: Subtract.
(9x8 + 2x7 + x6 – 4) – (9x8 + 4x7 + 5x6 – 1)
Answer by 10301650(25)   (Show Source):
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-2 x^7-4 x^6-3

Question 552685: I'm not sure how to simplify this fraction:
(8t)^3
------
8t^3
Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6103)   (Show Source):
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Simplify:
Cancel the 's to leave:
Cancel an 8 to get:

Answer by jim_thompson5910(21685)   (Show Source):
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(8t)^3
------
8t^3

512t^3
------
8t^3

64

So

(8t)^3
------ = 64
8t^3

Question 552173: how do i figure (-3) to the 4th power?
Answer by stanbon(48568)   (Show Source):
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how do i figure (-3) to the 4th power?
----
(-3)^4 = (-3)(-3)(-3)(-3) = (-1)^4*(3)^4 = 1*81 = 81
----
Cheers,
Stan H.
===========

Question 551873: what pattern do you discover when solving even-numbered exponents with negative bases?
is it:
A.Solution is always positive.
B.Solution is always negative.
C.Solution depends on the sign of the exponent.
D.None of the Above

Answer by edjones(7311)   (Show Source):
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(-1)^6=1
(-2)^2=4
(-3)^4=81
.
(-1)^-6=1
(-2)^-4=1/81
(-3)^-2=1/9
.
A
.
Ed

Question 551846: explain why 2 to the negative third power equals 1 over 2 to the third power

Answer by jim_thompson5910(21685)   (Show Source):
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This is because where k is some positive number.

Question 550919: Evaluate the following expression.
2^ -3
Answer by jim_thompson5910(21685)   (Show Source):
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2^(-3) = 1/(2^3) = 1/8

So 2^(-3)= 1/8

Question 550138: We have 4 hippos and we weigh them in pairs. After
weighing all possible pairs, we obtain the following list of
the weights of all pairs. Here is the list:
{356,362,374,374,386,392}
What is the sum of the weights of all the 4 hippos?
Answer by ankor@dixie-net.com(12704)   (Show Source):
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We have 4 hippos and we weigh them in pairs.
After weighing all possible pairs, we obtain the following list of
the weights of all pairs.
Here is the list:
{356, 362, 374, 374, 386, 392}
4 hippos a,b,c,d
;
a+b = 356
a+c = 362
a+d = 374
b+c = 374
b+d = 386
c+d = 392
:
Using the 1st two equations
a + 0 + c = 362
a + b + 0 = 356
-----------------subtraction eliminates a
-b + c = 6
c = (b+6)
using the 4th equation
b + c = 374
replace c with (b+6)
b + (b+6) = 374
2b = 374-6
2b = 368
b = 368/2
b = 184 kg is b's weight
then using the 1st equation
a + 184 = 356
a = 356 - 184
a = 172 kg is a's weight
:
Find c
c = 184 + 6
c = 190 kg is c's weight
:
find d
d + 190 = 392
d = 392 - 190
d = 202 kg is d's weight
"
find the sum
a = 172
b = 184
c = 190
d = 202
--------
sum 748 kg