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

2 Answers
SEric
Mar 2, 2018

You have to follow exponent laws in order to find the answer.

Explanation:

#(x^3)^4#
Becomes:

#x^(3*4)#

#= x^12#

Aviv S.
Mar 2, 2018

The answer is #x^12#.

Explanation:

Write out the whole power of #4#, then add up the exponents using the exponent addition rule. I color-coded some of the problem so that it is easier to see:

#color(white)=(x^3)^4#

#=(x^color(red)3)(x^color(yellow)3)(x^color(green)3)(x^color(blue)3)#

#=x^color(red)3*x^color(yellow)3*x^color(green)3*x^color(blue)3#

#=x^(color(red)3+color(yellow)3)*x^color(green)3*x^color(blue)3#

#=x^color(orange)6*x^color(green)3*x^color(blue)3#

#=x^(color(orange)6+color(green)3)*x^color(blue)3#

#=x^color(brown)9*x^color(blue)3#

#=x^(color(brown)9+color(blue)3)#

#=x^12#

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