How do you simplify #(16x^12 )^(3/4)#?

1 Answer
Karthik G
Feb 10, 2016

Steps are given below

Explanation:

#(16x^12)^(3/4)#

First let us go through some rules.

#quad quad quad color(blue)((a*b)^m=a^m*b^m#
#quad quad quad color(blue)((a^m)^n=a^(mn)#

For example

#(2x^2)^3 = 2^3*(x^2)^3#

#quad quad quad quad quad=8x^(2*3)#

#quad quad quad quad quad=8x^6#

Also let us write #16# as #2^4#

Our problem

#(16x^12)^(3/4)# becomes

#quadcolor(green)((2^4x^12)^(3/4)#

#color(green)(=(2^4)^(3/4)*(x^12)^(3/4)#
#color(green)(=2^(4xx3/4)*x^(12xx3/4)#

#color(green)(=2^3*x^9#

#color(green)(=8*x^9quad# Answer

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