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How would I solve

(x^3)^4? Would the answer be x^81 or x^27?

The outside exponent 4 confuses me. I remember choosing 27 but not sure why.

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2 Answers 2

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Neither. The answer is $x^3 \cdot x^3 \cdot x^3 \cdot x^3 = x^{3+3+3+3} = x^{3 \cdot 4} = x^{12}$.

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  • $\begingroup$ +2 - If I could. $\endgroup$
    – John Joy
    May 11, 2014 at 21:35
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The rule for expressions like this is $(x^a)^b = x^{ab}$. This is very different from $x^{a^b}$, obviously. What you would need to do in that case is apply the highest exponent first.

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