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Negative Exponents Inside and Outside of Parentheses

by Fran
(Nineveh, IN)











































How to work this problem:2x^3 y^2 z^4 Divided by x^7 y^-3 z^2 Parenthesis around the whole problem with an exponent -2 on the outside. I need to know the steps for solving this problem

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Jun 26, 2011
Negative Exponents Inside and Outside of Parentheses
by: Staff


The question:

by Fran
(Nineveh, IN)

How to work this problem:2x^3 y^2 z^4 Divided by x^7 y^-3 z^2 Parenthesis around the whole problem with an exponent -2 on the outside. I need to know the steps for solving this problem


The answer:

2x^3 y^2 z^4 Divided by x^7 y^-3 z^2 Parenthesis around the whole problem with an exponent -2 on the outside.

{[(2x^3) * (y^2) * ( z^4)]/[ (x^7) * (y^-3) * (z^2)]}^(-2)

= {[2 * (x^3) * (y^2) * ( z^4)]/[ (x^7) * (y^-3) * (z^2)]}^(-2)

= {2 * [(x^3)/(x^7)] * [(y^2)/(y^-3)] * [( z^4)/(z^2]}^(-2)

= {2 * [x^(3-7)] * [y^(2-(-3))] * [z^(4-2)]}^(-2)

= {2 * [x^(-4)] * [y^(5)] * [z^(2)]}^(-2)

= [2^(-2)] * [x^(-4)]^(-2)* [y^(5)]^(-2) * [z^(2)]^(-2)

= [2^(-2)] * [x^(8)] * [y^(-10)] * [z^(-4)]

= {1/[2^(2)]} * [x^(8)] * {1/[y^(10)]} * {1/[z^(4)]}

= (1/4) * [x^(8)] * {1/[y^(10)]} * {1/[z^(4)]}

= (1/4) * (x^8) * [1/(y^10)] * [1/(z^4]

= (x^8)/[4(y^10)(z^4)]

The final answer is:

(x^8)/[4(y^10)(z^4)]

or [4^(-1)](x^8)(y^(-10)(z^(-4)]



Thanks for writing.

Staff
www.solving-math-problems.com



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