How do you simplify (\frac { 2p ^ { - 2} q ^ { 3} } { 4p ^ { 8} q ^ { - 5} } ) ^ { - 5}?

1 Answer
Nov 27, 2017

(32p^50)/q^40

Explanation:

((2p^-2q^3)/(4p^8q^-5))^-5

First use the exponent rule (x^a)^b = x^(ab).

(2^-5p^10q^-15)/(4^-5p^-40q^25)

Use the exponent rule x^-a = 1/x^a and 1/x^-b = x^b.

(4^5p^10p^40)/(2^5q^25q^15)

Use the exponent rule x^a *x^b= x^(a+b)

(4^5p^50)/(2^5q^40)

Simplify the coefficients.

(1024p^50)/(32q^40)

Divide the coefficients.

(32p^50)/q^40