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Which expression is equivalent to $3^6 \times 7^6$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{21^6}$ $\newline$ (B) $21^{36}$ $\newline$ (C) $21^{12}$ $\newline$ (D) $21^6$

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Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

3^6 \times 7^6

?

\newline

Choices:

\newline

(A)

\frac{1}{21^6}

\newline

(B)

21^{36}

\newline

(C)

21^{12}

\newline

(D)

21^6

Recognize Property of Exponents: Recognize the property of exponents for multiplication with the same exponent but different bases. $\newline$ When multiplying powers with the same exponent but different bases, we can combine the bases and keep the exponent the same. $\newline$ $(a^m)(b^m) = (ab)^m$
Apply Property to Given Expression: Apply the property to the given expression $3^6 \times 7^6$ . Combine the bases and keep the exponent the same. $3^6 \times 7^6 = (3\times7)^6 = 21^6$
Match Result with Choices: Match the result with the given choices. $\newline$ The expression $21^6$ corresponds to choice (D).

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