How do you simplify #(- ( - a b ^ { 3} ) ^ { - 3} ) ^ { - 3} ( a ^ { 6} b ^ { 6} ) ^ { 2} ) ^ { 3}#?

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Answer 1 · 2018-06-06T16:03:34

#-a^63 * b^117#

the sign is - because the exponent +9 is odd.

#- a^{1 (-3)(-3)*3 + 6*2*3} * b^{3(-3)(-3)*3+6*2*3}#

#= -a^{+27+36} * b^{+81+36}#

Answer 2 · 2018-06-06T16:10:03

#a^63*b^117#

We make a step by step solution:
#(-ab^3)^(-3)=-a^(-3)*b^(-9)#
so we get
#-(-a^(-3)*b^(-9))=a^(-3)*b^(-9)#
then we get

#(a^(-3)b^(-9))^(-3)=a^9b^27#
and
#(a^6b^6)^3=a^12b^12#

and

#(a^9b^27a^12b^12)^3=(a^21b^39)^3=a^63b^117#