Which expression is equivalent to (3^(2)×3^(-1))^(2) ? 9 (1)/(9) 81 27

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

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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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Math Problems

Algebra 2

Simplify radical expressions with root inside the root

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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. $3^{2} = 3 \times 3 = 9$