How do you simplify ${(x^{3})}^{4}$ $(x^3)^4$ ?

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How do you simplify ${(x^{3})}^{4}$ $(x^3)^4$ ?

2 Answers

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Answer 1 · 2018-03-02T00:44:00

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

Explanation:

${(x^{3})}^{4}$ $(x^3)^4$
Becomes:

$x^{3 \cdot 4}$ $x^(3*4)$

$= x^{12}$ $= x^12$

Answer 2 · 2018-03-02T00:46:45

The answer is $x^{12}$ $x^12$ .

Explanation:

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

$= {(x^{3})}^{4}$ $color(white)=(x^3)^4$

$= (x^{3}) (x^{3}) (x^{3}) (x^{3})$ $=(x^color(red)3)(x^color(yellow)3)(x^color(green)3)(x^color(blue)3)$

$= x^{3} \cdot x^{3} \cdot x^{3} \cdot x^{3}$ $=x^color(red)3*x^color(yellow)3*x^color(green)3*x^color(blue)3$

$= x^{3 + 3} \cdot x^{3} \cdot x^{3}$ $=x^(color(red)3+color(yellow)3)*x^color(green)3*x^color(blue)3$

$= x^{6} \cdot x^{3} \cdot x^{3}$ $=x^color(orange)6*x^color(green)3*x^color(blue)3$

$= x^{6 + 3} \cdot x^{3}$ $=x^(color(orange)6+color(green)3)*x^color(blue)3$

$= x^{9} \cdot x^{3}$ $=x^color(brown)9*x^color(blue)3$

$= x^{9 + 3}$ $=x^(color(brown)9+color(blue)3)$

$= x^{12}$ $=x^12$

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How do you simplify ${(x^{3})}^{4}$ $(x^3)^4$ ?

2 Answers

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