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e
quad27^(2) as a power of 9

e $\quad 27^{2}$ as a power of $9$

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Evaluate integers raised to positive rational exponents

Full solution

Q. e

\quad 27^{2}

as a power of

9

Recognize Power of $9$ : Recognize that $27$ is a power of $9$ . $27 = 9 \times 3$ $= 3^3$
Rewrite Using Base: Rewrite $27$ using the base of $9$ . $\newline$ $27 = 3^3$ $\newline$ $= (9^{1/2})^3$
Apply Power Rule: Apply the power of a power rule. $\newline$ $(9^{\frac{1}{2}})^3 = 9^{\frac{3}{2}}$
Square to Find $27^2$ : Square the expression to find $27^2$ as a power of $9$ . $\newline$ $(9^{3/2})^2 = 9^{3/2 \times 2}$ $\newline$ $= 9^3$

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