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Which expression is equivalent to $(3^6)^4$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{3^{10}}$ $\newline$ (B) $3^{10}$ $\newline$ (C) $\frac{1}{3^{24}}$ $\newline$ (D) $3^{24}$

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Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

(3^6)^4

?

\newline

Choices:

\newline

(A)

\frac{1}{3^{10}}

\newline

(B)

3^{10}

\newline

(C)

\frac{1}{3^{24}}

\newline

(D)

3^{24}

Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{(m*n)}$ . We will apply this rule to the expression $(3^6)^4$ . $\newline$ $(3^6)^4 = 3^{(6*4)}$
Multiply Exponents: Multiply the exponents. $\newline$ Now we multiply the exponents $6$ and $4$ to find the new exponent for the base $3$ . $\newline$ $3^{(6*4)} = 3^{24}$
Match with Choices: Match the result with the given choices. $\newline$ We have found that $(3^6)^4$ is equal to $3^{24}$ . Now we look at the choices to find the equivalent expression. $\newline$ The correct choice that matches our result is (D) $3^{24}$ .

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