Which expression is equivalent to 8^6 * 9^6? Choices: (A)1/72^6 (B)72^12 (C)72^6 (D)72^36

Recognize Property of Exponents: Recognize the property of exponents for multiplication. 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 Numbers: Apply the property to 8^6 * 9^6. Combine the bases 8 and 9, and keep the exponent 6. 8^6 * 9^6 = (8*9)^6Calculate Product of Bases: Calculate the product of the bases 8 and 9. 8 * 9 = 72Write Expression with Combined Base: Write the expression with the combined base and exponent. (8*9)^6 = 72^6Match Result with Choices: Match the result with the given choices. 72^6 corresponds to choice (C) 72^6.

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

8^6 \times 9^6

\newline

Choices:

\newline

(A)

\frac{1}{72^6}

\newline

(B)

72^{12}

\newline

(C)

72^6

\newline

(D)

72^{36}

Recognize Property of Exponents: Recognize the property of exponents for multiplication. 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)^m
Apply Property to Given Numbers: Apply the property to \(8^6 \times 9^6. Combine the bases $8$ and $9$ , and keep the exponent $6$ . $8^6 \times 9^6 = (8\times9)^6$
Calculate Product of Bases: Calculate the product of the bases $8$ and $9$ . $\newline$ $8 \times 9 = 72$
Write Expression with Combined Base: Write the expression with the combined base and exponent. $\newline$ $(8\times9)^6 = 72^6$
Match Result with Choices: Match the result with the given choices. $72^6$ corresponds to choice (C) $72^6$ .