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

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Answer 1 · 2017-11-27T16:12:39

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

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

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.

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

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