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#