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Which expression is equivalent to $4^6 \times 3^6$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{12^6}$ $\newline$ (B) $12^{36}$ $\newline$ (C) $12^{12}$ $\newline$ (D) $12^6$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

4^6 \times 3^6

?

\newline

Choices:

\newline

(A)

\frac{1}{12^6}

\newline

(B)

12^{36}

\newline

(C)

12^{12}

\newline

(D)

12^6

Identify Bases and Exponents: Identify the base and the exponents in the given expression. $\newline$ In $4^6 \times 3^6$ , $4$ and $3$ are the bases raised to the exponent $6$ respectively. $\newline$ Base: $4$ , $3$ $\newline$ Exponents: $6$
Apply Exponent Rule: Use the property of exponents that states when multiplying two powers with the same exponent but different bases, you can multiply the bases and keep the exponent the same. $\newline$ $4^6 \times 3^6 = (4\times3)^6$ $\newline$ Calculate the product of the bases: $\newline$ $4 \times 3 = 12$
Calculate New Base: Rewrite the expression with the new base and the same exponent. $\newline$ $(4\times3)^6 = 12^6$
Match Result to Choices: Match the resulting expression with the given choices. $\newline$ The expression $12^6$ corresponds to choice (D) $12^6$ .

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