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Which expression is equivalent to
(3^(2)×3^(-1))^(2) ?
9

(1)/(9)
81
27

Which expression is equivalent to $\left(3^{2} \times 3^{-1}\right)^{2}$ ? $\newline$ $9$ $\newline$ $\frac{1}{9}$ $\newline$ $81$ $\newline$ $27$

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Simplify radical expressions with root inside the root

Full solution

Q. Which expression is equivalent to

\left(3^{2} \times 3^{-1}\right)^{2}

?

\newline

9

\newline

\frac{1}{9}

\newline

81

\newline

27

Simplify Exponents Using Properties: Simplify the expression inside the parentheses using the properties of exponents. $\newline$ The property of exponents we will use is that when we multiply powers with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $(3^{2}\times3^{-1}) = 3^{2-1} = 3^{1}$
Apply Power to Power Rule: Apply the power to a power rule to the simplified expression. $\newline$ The power to a power rule states that $(a^m)^n = a^{m*n}$ . $\newline$ $(3^{1})^{2} = 3^{1*2} = 3^{2}$
Calculate Final Value: Calculate the final value of the expression. $3^{2} = 3 \times 3 = 9$

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