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Which expression is equivalent to $(7^8)^7$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{7^{15}}$ $\newline$ (B) $\frac{1}{7^{56}}$ $\newline$ (C) $7^{56}$ $\newline$ (D) $7^{15}$

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Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

(7^8)^7

?

\newline

Choices:

\newline

(A)

\frac{1}{7^{15}}

\newline

(B)

\frac{1}{7^{56}}

\newline

(C)

7^{56}

\newline

(D)

7^{15}

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, $(7^8)^7 = 7^{(8*7)}$ .
Calculate new exponent: Calculate the exponent. $\newline$ Multiply the exponents $8$ and $7$ to find the new exponent. $\newline$ $7^{(8*7)} = 7^{56}$ .
Match with choices: Match the result with the given choices. $\newline$ The calculation from Step $2$ gives us $7^{56}$ , which matches choice $(C)$ .

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