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Which expression is equivalent to $2^7 \times 2^2$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{2^9}$ $\newline$ (B) $2^9$ $\newline$ (C) $2^{14}$ $\newline$ (D) $\frac{1}{2^{14}}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

2^7 \times 2^2

?

\newline

Choices:

\newline

(A)

\frac{1}{2^9}

\newline

(B)

2^9

\newline

(C)

2^{14}

\newline

(D)

\frac{1}{2^{14}}

Identify Base and Exponents: Identify the base and the exponents in the expression $2^7 \times 2^2$ . $\newline$ Base: $2$ $\newline$ Exponents: $7, 2$
Combine Exponents: Combine the exponents by adding them, since the bases are the same. $\newline$ $2^7 \times 2^2 = 2^{(7+2)} = 2^9$
Match with Choices: Match the result with the given choices. $\newline$ $2^9$ corresponds to choice (B).

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