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Select all the expressions that are equivalent to $3^4 \times 7^4$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{21^{-4}}$ $\newline$ (B) $21^8$ $\newline$ (C) $21^{16}$ $\newline$ (D) $21^4$

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Negative exponents

Full solution

Q. Select all the expressions that are equivalent to

3^4 \times 7^4

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{21^{-4}}

\newline

(B)

21^8

\newline

(C)

21^{16}

\newline

(D)

21^4

Calculate Exponents: Step $1$ : Calculate $3^4 \times 7^4$ . Using the property of exponents $(a^m)\times(b^m) = (a\times b)^m$ , we can rewrite $3^4 \times 7^4$ as $(3\times7)^4$ . Calculation: $3\times7 = 21$ , so $3^4 \times 7^4 = 21^4$ .
Compare Choices: Step $2$ : Compare with the choices. $\newline$ (A) $\frac{1}{21^{-4}}$ simplifies to $21^4$ using the negative exponent rule $a^{-m} = \frac{1}{a^m}$ . $\newline$ (B) $21^8$ is not equal to $21^4$ because the exponents are different. $\newline$ (C) $21^{16}$ is also not equal to $21^4$ for the same reason. $\newline$ (D) $21^4$ is exactly what we calculated.

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