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mike88

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posted by mike88 on 10/13/2008 3:26:08 AM | status: Live

Urgent!!! Please help!! Will rate high!

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Question Details:

The expression $\displaystyle \left (\frac{x^4 y^2 z^5 x^{-5}}{x^4 y^3 z^4 y^2}\right )^{-3}$ equals

where

, the exponent of

, is:
and

, the exponent of

, is:
and finally

, the exponent of

, is:
[NOTE: Your answers cannot be algebraic expressions.]

Tags: Algebra thru Pre-Calculus

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Answers:

rapunzel

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posted by rapunzel on 10/13/2008 3:49:49 AM | status: Live

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Response Details:

First simplify within the parenthases by adding any exponents on the top together (when they have the same base) and subtracting any on the bottom:

(x^{4 + -5 - 4}y^{2 - 3 - 2} z^{5 - 4})^-3

(x^-5y^-3 z¹)^-3

When you raise an exponent to another exponent, you multiply the numbers:

x¹⁵y⁹ z^-3

r = 15
s = 9
t = -3

Good Luck!

KAT13

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posted by KAT13 on 10/13/2008 4:16:57 AM | status: Live

Asker's Rating: Helpful

Response Details:

I just double checked the above solution and it is correct. you could also do the above and bottom of the solution seperately and then subtract the top exponents minus the bottom exponents.

(x^4+-5)^-3(y²)^-3(z⁵)^-3=x³y^-6z^-15 because you multiply exponents inside the parenthesis by -3 for each component.

Then, for the bottom, (x^-4)^-3(y^-3-2)^-3(z^-4)^-3=x¹²y¹⁵z¹², since the bottom exponents are just the negative of the top exponents.

Then, just add the top and bottom. so, x¹²⁺³y^-6+15z^-15+12=x¹⁵y⁹z^-3, therefore, r=15, s=9, t=-3