Select all the expressions that are equivalent to 3^4 * 7^4. Multi-select Choices: (A)1/21^-4 (B)21^8 (C)21^16 (D)21^4

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

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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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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.