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

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Answer 1 · 2017-12-01T16:27:54

#-200x^8y^9#

#(-2x^2y)^color(red)3(5xy^3)^color(blue)2#

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

#((-2)^color(red)3x^(2*color(red)3)y^(1*color(red)3))(5^color(blue)2x^(1*color(blue)2)y^(3*color(blue)2))#

Simplify.

#(-8x^6y^3)(25x^2y^6)#

Multiply the coefficients #-8# and #25#

#-200(x^color(red)6y^color(blue)3)(x^color(red)2y^color(blue)6)#

Next, use the exponent rule #x^a *x^b = x^(ab)#

#-200x^((color(red)(6+2)))y^((color(blue)(3+6)))#

#-200x^8y^9#