Which expression is equivalent to 3^5 * 2^5? Choices: (A)1/6^5 (B)6^10 (C)6^5 (D)6^25

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

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

3^5 \times 2^5

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Choices:

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(A)

\frac{1}{6^5}

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(B)

6^{10}

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(C)

6^5

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(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).