How do you simplify #\frac { f ^ { 9} g ^ { - 52} } { f ^ { - 1} g ^ { - 9} \cdot f ^ { 3} g ^ { 76} }#?

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Answer 1 · 2017-10-21T12:15:47

#f^7 g^-119#

#(f^9 g^-52)/(f^-1 g^-9 cdot f^3 g^76)#

Solving the denominator first..

#(f^9 g^-52)/color(red)(f^-1 g^-9 cdot f^3 g^76)#

#(f^9 g^-52)/color(red)(f^-1 xx f^3 cdot g^-9 xx g^76)#

Recall, #a^x xx a^y = a^(x + y) and a^x div a^y = a^(x - y)#

#(f^9 g^-52)/color(red)(f^(-1 + 3) cdot g^(-9 + 76)#

#(f^9 g^-52)/color(red)(f^2 cdot g^67#

#f^9 g^-52 div f^2 g^67#

#f^(9 - 2) g^(-52 - 67)#

#f^7 g^-119#