Which expression is equivalent to 3^6 * 7^6? Choices: (A)1/21^6 (B)21^36 (C)21^12 (D)21^6

Recognize Property of Exponents: Recognize the property of exponents for multiplication with the same exponent but different bases. When multiplying powers with the same exponent but different bases, we can combine the bases and keep the exponent the same. (a^m)(b^m) = (ab)^mApply Property to Given Expression: Apply the property to the given expression 3^6 * 7^6. Combine the bases and keep the exponent the same. 3^6 * 7^6 = (3*7)^6 = 21^6Match Result with Choices: Match the result with the given choices. The expression 21^6 corresponds to choice (D).

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Which expression is equivalent to $3^6 \times 7^6$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{21^6}$ $\newline$ (B) $21^{36}$ $\newline$ (C) $21^{12}$ $\newline$ (D) $21^6$

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

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Q. Which expression is equivalent to

3^6 \times 7^6

\newline

Choices:

\newline

(A)

\frac{1}{21^6}

\newline

(B)

21^{36}

\newline

(C)

21^{12}

\newline

(D)

21^6

Recognize Property of Exponents: Recognize the property of exponents for multiplication with the same exponent but different bases. $\newline$ When multiplying powers with the same exponent but different bases, we can combine the bases and keep the exponent the same. $\newline$ $(a^m)(b^m) = (ab)^m$
Apply Property to Given Expression: Apply the property to the given expression $3^6 \times 7^6$ . Combine the bases and keep the exponent the same. $3^6 \times 7^6 = (3\times7)^6 = 21^6$
Match Result with Choices: Match the result with the given choices. $\newline$ The expression $21^6$ corresponds to choice (D).