How do you simplify #((-30a^14 b^8) /( 10a^17 b^-2))^3#?

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Answer 1 · 2016-12-22T15:20:06

#=-(27b^30)/a^9#

First deal with what is inside the brackets

Write as #(-1)xx30/10xxa^14/a^17xxb^8/b^(-2)#

#(-1)xx3xx(cancel(a^14))/(cancel(a^14)xxa^3)xxb^8xxb^2#

#(-1)xx3xx1/a^3xxb^10#

Putting it all together

#- (3b^10)/a^3#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So #(-(30a ^14b^8)/(10a^17b^(-2)))^3" "=" "(- (3b^10)/a^3)^3#

#=(-1)^3xx3^3xx((b^10)/(a^3))^3#

#-1xx27xxb^30/a^9#

#=-(27b^30)/a^9#