Which expression is equivalent to (7^4)^6? Choices: (A)7^10 (B)7^24 (C)1/7^10 (D)1/7^24

Apply power rule: Apply the power of a power rule. The power of a power rule states that (a^m)^n = a^(m*n). So, (7^4)^6 = 7^(4*6).Calculate exponent: Calculate the exponent. Multiply the exponents 4 and 6 to find the equivalent expression. 7^(4*6) = 7^24.Match with choices: Match the result with the given choices. The calculation from Step 2 gives us 7^24, which corresponds to choice (B).

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Which expression is equivalent to $(7^4)^6$ ? $\newline$ Choices: $\newline$ (A) $7^{10}$ $\newline$ (B) $7^{24}$ $\newline$ (C) $\frac{1}{7^{10}}$ $\newline$ (D) $\frac{1}{7^{24}}$

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

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Q. Which expression is equivalent to

(7^4)^6

\newline

Choices:

\newline

(A)

7^{10}

\newline

(B)

7^{24}

\newline

(C)

\frac{1}{7^{10}}

\newline

(D)

\frac{1}{7^{24}}

Apply power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{(m*n)}$ . $\newline$ So, $(7^4)^6 = 7^{(4*6)}$ .
Calculate exponent: Calculate the exponent. $\newline$ Multiply the exponents $4$ and $6$ to find the equivalent expression. $\newline$ $7^{(4*6)} = 7^{24}$ .
Match with choices: Match the result with the given choices. $\newline$ The calculation from Step $2$ gives us $7^{24}$ , which corresponds to choice $(B)$ .