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Which expression is equivalent to $7^4 \times 3^4$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{21^4}$ $\newline$ (B) $21^4$ $\newline$ (C) $21^{16}$ $\newline$ (D) $21^8$

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Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

7^4 \times 3^4

?

\newline

Choices:

\newline

(A)

\frac{1}{21^4}

\newline

(B)

21^4

\newline

(C)

21^{16}

\newline

(D)

21^8

Understand Exponent Properties: Understand the properties of exponents. $\newline$ When multiplying powers with the same exponent but different bases, we can multiply the bases first and then apply the exponent to the result. $\newline$ $(a^m)(b^m) = (ab)^m$
Apply Property to Multiplication: Apply the property to $7^4 \times 3^4$ . $\newline$ Multiply the bases ( $7$ and $3$ ) and then apply the exponent $4$ . $\newline$ $(7^4)(3^4) = (7\times3)^4$ $\newline$ $= 21^4$
Match Result with Choices: Match the result with the given choices. $\newline$ The expression $21^4$ corresponds to choice (B).

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