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Which expression is equivalent to $3^5 \times 2^5$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{6^5}$ $\newline$ (B) $6^{10}$ $\newline$ (C) $6^5$ $\newline$ (D) $6^{25}$

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Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

3^5 \times 2^5

?

\newline

Choices:

\newline

(A)

\frac{1}{6^5}

\newline

(B)

6^{10}

\newline

(C)

6^5

\newline

(D)

6^{25}

Understand Exponent Properties: Understand the properties of exponents. $\newline$ When multiplying powers with the same exponent but different bases, we can combine the bases and keep the exponent. $\newline$ (a^m)(b^m) = (ab)^m
Apply Property to Expression: Apply the property to the given expression.\(\newlineCombine the bases $3$ and $2$ , and keep the exponent $5$ . $\newline$ $3^5 \times 2^5 = (3\times2)^5$
Calculate Base: Calculate the base. $\newline$ Multiply the bases $3$ and $2$ . $\newline$ $3 \times 2 = 6$
Apply Base to Exponent: Apply the base to the exponent. $\newline$ Now that we have the base calculated, apply it to the exponent $5$ . $\newline$ $(3\times2)^5 = 6^5$
Match Result with Choices: Match the result with the given choices. $\newline$ The expression $6^5$ matches with choice (C).

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