Which expression is equivalent to (3^6)^9? Choices: (A)3^15 (B)1/3^15 (C)1/3^54 (D)3^54

Apply power rule: Apply the power of a power rule. What operation should we perform with the exponents, 6 and 9? When we raise a power to another power, we multiply the exponents. (a^m)^n = a^(m * n)Calculate new exponent: Calculate the new exponent by multiplying the exponents 6 and 9. (3^6)^9 = 3^(6 * 9) = 3^54Choose equivalent expression: Choose the equivalent expression for (3^6)^9. (3^6)^9 = 3^54 The equivalent expression is 3^54.

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Which expression is equivalent to $(3^6)^9$ ? $\newline$ Choices: $\newline$ (A) $3^{15}$ $\newline$ (B) $\frac{1}{3^{15}}$ $\newline$ (C) $\frac{1}{3^{54}}$ $\newline$ (D) $3^{54}$

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Math Problems

Algebra 1

Identify equivalent exponential expressions I

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Q. Which expression is equivalent to

(3^6)^9

\newline

Choices:

\newline

(A)

3^{15}

\newline

(B)

\frac{1}{3^{15}}

\newline

(C)

\frac{1}{3^{54}}

\newline

(D)

3^{54}

Apply power rule: Apply the power of a power rule. $\newline$ What operation should we perform with the exponents, $6$ and $9$ ? $\newline$ When we raise a power to another power, we multiply the exponents. $\newline$ $(a^m)^n = a^{(m \times n)}$
Calculate new exponent: Calculate the new exponent by multiplying the exponents $6$ and $9$ . $\newline$ $(3^6)^9 = 3^{(6 \times 9)}$ $\newline$ $= 3^{54}$
Choose equivalent expression: Choose the equivalent expression for $(3^6)^9$ . $(3^6)^9 = 3^{54}$ The equivalent expression is $3^{54}$ .