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Which expression is equivalent to $7^4 \times 2^4$ ? $\newline$ Choices: $\newline$ (A) $14^4$ $\newline$ (B) $14^8$ $\newline$ (C) $\frac{1}{14^4}$ $\newline$ (D) $14^{16}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

7^4 \times 2^4

?

\newline

Choices:

\newline

(A)

14^4

\newline

(B)

14^8

\newline

(C)

\frac{1}{14^4}

\newline

(D)

14^{16}

Identify Bases and Exponents: Identify the bases and the exponents in the expression $7^4 \times 2^4$ . We have two bases, $7$ and $2$ , each raised to the exponent $4$ . Base $1$ : $7$ Exponent $1$ : $4$ Base $2$ : $2$ Exponent $2$ : $4$
Apply Exponent Property: Apply the property of exponents for multiplication with the same exponent but different bases. $\newline$ When we multiply two powers with the same exponent but different bases, we can combine the bases and keep the exponent the same. $\newline$ $7^4 \times 2^4 = (7 \times 2)^4$
Calculate Base Product: Calculate the product of the bases. $\newline$ Multiply the bases $7$ and $2$ . $\newline$ $7 \times 2 = 14$
Write Combined Expression: Write the expression with the combined base and the same exponent. $\newline$ $(7 \times 2)^4 = 14^4$
Choose Equivalent Expression: Choose the equivalent expression for $7^4 \times 2^4$ . From the calculations above, we can see that $7^4 \times 2^4$ is equivalent to $14^4$ .

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