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Express
[(3^(2))^(4)]^(3) as a single power of 3

Express $\left[\left(3^{2}\right)^{4}\right]^{3}$ as a single power of $3$

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Multiplication with rational exponents

Full solution

Q. Express

\left[\left(3^{2}\right)^{4}\right]^{3}

as a single power of

3

Apply power rule: First, apply the power of a power rule which states that $(a^m)^n = a^{(m*n)}$ . $\newline$ So, $[(3^{2})^{4}]^{3}$ becomes $3^{(2*4*3)}$ .
Multiply exponents: Now, multiply the exponents: $2 \times 4 \times 3 = 24$ . So, we have $3^{24}$ .
Final result: There's no need to simplify further, $3^{24}$ is already a single power of $3$ .

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