Which expression is equivalent to 7^5 * 2^5? Choices: (A)14^25 (B)14^10 (C)1/14^5 (D)14^5

Apply Rule for Multiplying Powers: Apply the rule for multiplying powers with the same exponent but different bases. According to the rule (a^m)*(b^m) = (a*b)^m, we can combine the bases and keep the exponent the same. So, 7^5 * 2^5 becomes (7*2)^5.Calculate Product of Bases: Calculate the product of the bases. Multiply the bases 7 and 2 to get 14. 7*2 = 14Apply Exponent to Product: Apply the product of the bases to the exponent. Now that we have the product of the bases, we apply the exponent 5 to it. (7*2)^5 = 14^5Match Result with Choices: Match the result with the given choices. The expression 14^5 matches with choice (D).

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

7^5 \times 2^5

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Choices:

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(A)

14^{25}

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(B)

14^{10}

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(C)

\frac{1}{14^5}

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(D)

14^5

Apply Rule for Multiplying Powers: Apply the rule for multiplying powers with the same exponent but different bases. $\newline$ According to the rule $(a^m)\cdot(b^m) = (a\cdot b)^m$ , we can combine the bases and keep the exponent the same. $\newline$ So, $7^5 \cdot 2^5$ becomes $(7\cdot2)^5$ .
Calculate Product of Bases: Calculate the product of the bases. $\newline$ Multiply the bases $7$ and $2$ to get $14$ . $\newline$ $7 \times 2 = 14$
Apply Exponent to Product: Apply the product of the bases to the exponent. $\newline$ Now that we have the product of the bases, we apply the exponent $5$ to it. $\newline$ $(7\times2)^5 = 14^5$
Match Result with Choices: Match the result with the given choices. $\newline$ The expression $14^5$ matches with choice (D).