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Which expression is equivalent to $12^2 \times 12^4$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{12^6}$ $\newline$ (B) $\frac{1}{12^8}$ $\newline$ (C) $12^8$ $\newline$ (D) $12^6$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

12^2 \times 12^4

?

\newline

Choices:

\newline

(A)

\frac{1}{12^6}

\newline

(B)

\frac{1}{12^8}

\newline

(C)

12^8

\newline

(D)

12^6

Identify Base and Exponents: Identify the base and the exponents. $\newline$ In the expression $12^2 \times 12^4$ , $12$ is the base raised to the exponents $2$ and $4$ respectively. $\newline$ Base: $12$ $\newline$ Exponents: $2$ , $4$
Combine Exponents: Combine the exponents. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $12^2 \times 12^4 = 12^{2+4} = 12^6$
Simplify Expression: Simplify the expression. $\newline$ Since we have combined the exponents, the expression simplifies to $12$ raised to the power of $6$ . $\newline$ $12^2 \times 12^4 = 12^6$
Choose Equivalent Expression: Choose the equivalent expression for $12^2 \times 12^4$ . From the given choices, $12^6$ is the correct equivalent expression. So, the answer is (D) $12^6$ .

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