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Which expression is equivalent to $6^8 \times 6^7$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{6^{15}}$ $\newline$ (B) $\frac{1}{6^{56}}$ $\newline$ (C) $6^{56}$ $\newline$ (D) $6^{15}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

6^8 \times 6^7

?

\newline

Choices:

\newline

(A)

\frac{1}{6^{15}}

\newline

(B)

\frac{1}{6^{56}}

\newline

(C)

6^{56}

\newline

(D)

6^{15}

Identify Base and Exponents: Identify the base and the exponents. $\newline$ In $6^8$ and $6^7$ , $6$ is the base raised to the exponents $8$ and $7$ respectively. $\newline$ Base: $6$ $\newline$ Exponents: $8$ , $7$
Rewrite Expression: Given expression: $6^8 \times 6^7$ $\newline$ Rewrite this expression as a single power of $6$ . $\newline$ When we multiply powers with the same base, we add the exponents. $\newline$ $6^8 \times 6^7$ $\newline$ $= 6^{8+7}$ $\newline$ $= 6^{15}$
Choose Equivalent Expression: Choose the equivalent expression for $6^8 \times 6^7$ . $\newline$ $6^8 \times 6^7 = 6^{15}$ $\newline$ So, the equivalent expression is $6^{15}$ , which corresponds to choice (D).

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