A fraction with negative exponents

Math Central

Quandaries & Queries

Question from Gabriel, a student:

What does the line separating the top from the bottom mean? what does it tell you to do and what is the answer to the question?

Question 3

Simplify. Write the answer using only positive exponents. Assume all variables represent nonzero numbers.

(x^-5)^-4(x^-1y)^3
________________
(xy^4)^3

Hi Gabriel,

I am going to solve a similar problem.

Simplify. Write the answer using only positive exponents. Assume all variables represent nonzero numbers.
$fraction$

I would first remove the parentheses remembering the two laws of exponents that say

(a^b)^c = a^bcand a^ba^c = a^bc.

I get

$fraction$

We are not done yet as there are negative exponents. Now I need to use the fact that

$fraction$

Hence I get

$fraction$

I hope this helps,

Penny

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