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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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Identify equivalent exponential expressions II

Full solution

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 $(B)$ .

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