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Which expression is equivalent to $3^2 \times 3^4$ ? $\newline$ Choices: $\newline$ (A) $3^8$ $\newline$ (B) $\frac{1}{3^6}$ $\newline$ (C) $3^6$ $\newline$ (D) $\frac{1}{3^8}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

3^2 \times 3^4

?

\newline

Choices:

\newline

(A)

3^8

\newline

(B)

\frac{1}{3^6}

\newline

(C)

3^6

\newline

(D)

\frac{1}{3^8}

Identify Base and Exponents: Identify the base and the exponents in the expression $3^2 \times 3^4$ . The base is $3$ , and the exponents are $2$ and $4$ , respectively. Base: $3$ Exponents: $2$ , $4$
Apply Multiplication Rule: Apply the rule for multiplying powers with the same base. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $3^2 \times 3^4 = 3^{(2+4)}$
Perform Exponent Addition: Perform the addition of the exponents. $3^{2+4} = 3^6$
Choose Equivalent Expression: Choose the equivalent expression for $3^2 \times 3^4$ . The equivalent expression is $3^6$ .

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