SOLUTION: please help me simplify these expressions leaving the final answer with only positive exponents: 1. {{{(x^4y^(-5))/(x^(-8)z^2)^(-m)}}} 2. {{{((2x^(-5)y)/(y^(-8)*z^(-5)))^(

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: please help me simplify these expressions leaving the final answer with only positive exponents: 1. {{{(x^4y^(-5))/(x^(-8)z^2)^(-m)}}} 2. {{{((2x^(-5)y)/(y^(-8)*z^(-5)))^(      Log On


   

Question 209010: please help me simplify these expressions leaving
the final answer with only positive exponents:
1. %28x%5E4y%5E%28-5%29%29%2F%28x%5E%28-8%29z%5E2%29%5E%28-m%29
2. %28%282x%5E%28-5%29y%29%2F%28y%5E%28-8%29%2Az%5E%28-5%29%29%29%5E%28-3%29

I'll wait for your reply sir/madam. It will be a great help for my homework. Thank you.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(x^4 y^-5/x^-8 z^2)^-m (2x^-5y/y^-8 z^-5)^-3
---
= (x^12/y^5z^2)^-m (2y^8z^5/x^5)^-3
---
= (y^5z^2/x^12)^m (x^5/2y^8z^5)^3
---
= (y^5m*z^2m/x^12m) (x^15/(8*y^24*z^15))
---
= x^(15-12m) * y^(5m-24) *z^(2m-15)
============================================
Cheers,
Stan H.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
please help me solve this equation: 

%28x%5E4y%5E%28-5%29%29%2F%28x%5E%28-8%29z%5E2%29%5E%28-m%29  

Remove the parentheses on the bottom by multiplying
each inner exponent by the outer exponent -m

%28x%5E4y%5E%28-5%29%29%2F%28x%5E%28%28-8%29%28-m%29%29z%5E%28%282%29%28-m%29%29%29

%28x%5E4y%5E%28-5%29%29%2F%28x%5E%288m%29z%5E%28-2m%29%29

Get rid of the negative exponents by 
1. Move them up or down across the fraction bar
2. Change the sign of the exponent to positive:

In this case we move the y%5E%28-5%29 down to
the bottom as y%5E5 and we move the z%5E%28-2m%29
up to the top as z%5E%282m%29 

%28x%5E4z%5E%282m%29%29%2F%28x%5E%288m%29y%5E5%29

Now subtract exponents of the x's

%28x%5E%284-8m%29z%5E%282m%29%29%2F%28y%5E5%29

or if you prefer you can subtract
exponents the other way and get

z%5E%282m%29%2F%28x%5E%288m-4%29y%5E5%29

Either is correct since they are
equivalent.

=======================================

%28%282x%5E%28-5%29y%29%2F%28y%5E%28-8%29%2Az%5E%28-5%29%29%29%5E%28-3%29 

Make sure every factor in both numerator
shows its exponent, whether it is a number 
or a letter, and even if it has exponent 1:

%28%282%5E1x%5E%28-5%29y%5E1%29%2F%28y%5E%28-8%29%2Az%5E%28-5%29%29%29%5E%28-3%29 

Remove the parentheses by multiplying each
of the five inside exponents by the outside
exponent -3:



+%282%5E%28-3%29x%5E%2815%29y%5E%28-3%29%29%2F%28y%5E24%2Az%5E15%29++%29

Now we only have to move the factors with negative
exponents from top to bottom and change the signs
of the exponents to positive:

+x%5E15%2F%282%5E3%2Ay%5E3%2Ay%5E24%2Az%5E15%29++%29

Finally we write 2%5E3 as 8
and add exponents of y:

+x%5E15%2F%288%2Ay%5E27%2Az%5E15%29++%29

Edwin