How do you simplify #((-gh^4)/(g^3h))^7#?

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Answer 1 · 2018-07-09T22:10:51

#-\frac{h^21}{g^14}#

Given that

#(\frac{-gh^4}{g^3h})^7#

#=(-1)^7(\frac{gh^4}{g^3h})^7#

#=-(gh^4\cdot g^{-3}h^{-1})^7#

#=-(g^{1-3}h^{4-1})^7#

#=-(g^{-2}h^{3})^7#

#=-(g^{-2})^7(h^3)^7#

#=-g^{-14}h^{21}#

#=-\frac{h^21}{g^14}#

Answer 2 · 2018-07-09T22:17:08

#= -h^21/g^14#

Given: #((-gh^4)/(g^3h))^7#

Use the exponent rules: #x^m/x^n = x^(m-n) " or "1/x^(n-m)#

#(x/y)^n = x^n/y^n " and " (x^n)^m = x^(n*m)#

#((-gh^4)/(g^3h))^7 =( (-h^(4-1))/(g^(3-1)))^7 = ((-h^3)/g^2)^7#

#= -h^21/g^14#