How do you simplify #(x^-4)^5(x^3y^2)^5#?

1 Answer
Nov 1, 2015

Answer:

#x^{-5}y^{10}#

Explanation:

First rule to use: the power of powers means to multiply the exponents, so

  1. #(x^{-4})^5 = x^{-4*5} = x^{-20}#
  2. #(x^3y^2)^5 = x^{3*5}y^{2*5} = x^{15}y^{10}#

So, your expression becomes

#x^{-20}*x^{15}y^{10}#

Second rule to use: the product of powers with the same base means to sum the exponents. So, the #y# power is alone and we'll leave it untouched. As for the #x# powers, we have

#x^{-20}*x^{15} = x^{-20+15}=x^{-5}#.