How do you simplify #(2gh^4)^3[(-2g^4h)^3]^2#?

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Answer 1 · 2017-05-28T21:36:25

#512g^(27)h^(18)#

Start by taking the outside exponents and multiplying them through:

#(2gh^4)^(color(red)(3))[(-2g^4h)^3]^(color(red)(2))#

#=(2^(color(red)(3))g^(color(red)(3))h^(4xxcolor(red)(3)))[(-2g^4h)^(3xxcolor(red)(2))]#

Simplify

#=(8g^(3)h^12)[(-2g^4h)^(6)]#

Next, take the outside exponent of #6# and multiply it through:

#=(8g^(3)h^12)[(-2g^4h)^(color(blue)(6))]#

#=(8g^(3)h^12)((-2)^(color(blue)(6))g^(4xxcolor(blue)(6))h^(color(blue)(6)))#

Simplify

#=(8g^(3)h^12)((-2)^(color(blue)(6))g^(4xxcolor(blue)(6))h^(color(blue)(6)))#

#=(8g^(3)h^12)(64g^(24)h^(6))#

When multiplying two identical bases with different exponents, you add the exponents over a single base.

#=8xx64g^(3)g^(24)h^(12)h^(6)#

#=512g^(3+24)h^(12+6)#

#=512g^(27)h^(18)#