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Which expression is equivalent to $3^6 \times 3^8$ ? $\newline$ Choices: $\newline$ (A) $3^{48}$ $\newline$ (B) $\frac{1}{3^{48}}$ $\newline$ (C) $3^{14}$ $\newline$ (D) $\frac{1}{3^{14}}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

3^6 \times 3^8

?

\newline

Choices:

\newline

(A)

3^{48}

\newline

(B)

\frac{1}{3^{48}}

\newline

(C)

3^{14}

\newline

(D)

\frac{1}{3^{14}}

Identify Base and Exponents: Identify the base and the exponents. $\newline$ In the expression $3^6 \times 3^8$ , the base is $3$ , and it is raised to the exponents $6$ and $8$ , respectively. $\newline$ Base: $3$ $\newline$ Exponents: $6, 8$
Apply Multiplication Rule: Apply the rule for multiplying powers with the same base. $\newline$ When we multiply powers with the same base, we add the exponents. $\newline$ $3^6 \times 3^8 = 3^{(6+8)}$
Perform Exponents Addition: Perform the addition of the exponents. $\newline$ Calculate the sum of the exponents $6$ and $8$ . $\newline$ $6 + 8 = 14$
Rewrite Expression with Combined Exponent: Rewrite the expression with the combined exponent. $\newline$ Replace the sum of the exponents in the expression. $\newline$ $3^6 \times 3^8 = 3^{14}$
Choose Equivalent Expression: Choose the equivalent expression for $3^6 \times 3^8$ . $\newline$ From the given choices, $3^{14}$ is the correct equivalent expression. $\newline$ So, the final answer is (C) $3^{14}$ .

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