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Which expression is equivalent to $5^4 \times 3^4$ ? $\newline$ Choices: $\newline$ (A) $15^8$ $\newline$ (B) $15^4$ $\newline$ (C) $15^{16}$ $\newline$ (D) $\frac{1}{15^4}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

5^4 \times 3^4

?

\newline

Choices:

\newline

(A)

15^8

\newline

(B)

15^4

\newline

(C)

15^{16}

\newline

(D)

\frac{1}{15^4}

Identify Bases and Exponents: Identify the bases and the exponents in the expression $5^4 \times 3^4$ . We have two bases, $5$ and $3$ , each raised to the exponent $4$ . Bases: $5$ , $3$ Exponents: $4$
Apply Product of Powers Property: Apply the product of powers property for multiplication of expressions with the same exponent but different bases. $\newline$ The product of powers property states that $(a^m)(b^m) = (ab)^m$ . $\newline$ So, $5^4 \times 3^4 = (5\times3)^4$
Calculate Product of Bases: Calculate the product of the bases. $5 \times 3 = 15$
Apply Product to Exponent: Apply the product of the bases to the exponent. $\newline$ $(5\times3)^4 = 15^4$
Choose Equivalent Expression: Choose the equivalent expression for $5^4 \times 3^4$ . $5^4 \times 3^4$ is equivalent to $15^4$ .

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