How do you simplify #(\frac { 3b ^ { 4} } { a ^ { 2} } ) ^ { 5}#?

1 Answer
EZ as pi
Nov 5, 2016

#(243b^20)/a^10#

Explanation:

The index of #5# means that there are 5 of the same bracket multiplied together. Luckily we do not have to do this the long method, there are laws of indices which we can apply.

Note that in the bracket there is a number (3) and variables with indices. They are treated differently.

Recall:
#(xy)^m = x^m y^m " "and (x^m)^n = x^(mn)" "larr#multiply the indices

#((3b^4)/a^2)^5 = (3^5 b^(4xx5))/a^(2xx5)#

#= (3^5b^20)/a^10" "larr 3^5 = 3*3*3*3*3#

#(243b^20)/a^10#

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