How do you simplify #\frac { x ^ { - 8} ( x ^ { - 2} y ^ { 2} ) ^ { 2} } { ( 4x ^ { - 4} ) ^ { 2} y ^ { 2} }#?

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Answer 1 · 2018-04-23T00:47:17

#(x^-8(x^-2y^2)^2)/((4x^-4)^2y^2)=y^2/(16x^4)#

#(x^-8(x^-2y^2)^2)/((4x^-4)^2y^2)#

Let's loose the parenthesis first. Remember that

#(x^m)^n=x^(mn)#.

#(x^-8(x^-2y^2)^2)/((4x^-4)^2y^2)= (x^-8x^-4y^4)/(16x^-8y^2)#

Now cancel. Remember that

#(x^m)/(x^n)=x^(m-n)#.

#(x^-8x^-4y^4)/(16x^-8y^2)=(x^-4y^2)/16#

Now express everything with positive exponents. Remember that

#x^-m=1/x^m#

#(x^-4y^2)/16=y^2/(16x^4)#