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Which expression is equivalent to $2^7 \times 2^3$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{2^{21}}$ $\newline$ (B) $2^{10}$ $\newline$ (C) $\frac{1}{2^{10}}$ $\newline$ (D) $2^{21}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

2^7 \times 2^3

?

\newline

Choices:

\newline

(A)

\frac{1}{2^{21}}

\newline

(B)

2^{10}

\newline

(C)

\frac{1}{2^{10}}

\newline

(D)

2^{21}

Identify Base and Exponents: Identify the base and the exponents. $\newline$ In $2^7$ and $2^3$ , $2$ is the base raised to the exponents $7$ and $3$ respectively. $\newline$ Base: $2$ $\newline$ Exponents: $7$ , $3$
Rewrite Expression as Single Power: Given expression: $2^7 \times 2^3$ $\newline$ Rewrite this expression as a single power of $2$ . $\newline$ When we multiply powers with the same base, we add the exponents. $\newline$ $2^7 \times 2^3$ $\newline$ $= 2^{7+3}$ $\newline$ $= 2^{10}$
Choose Equivalent Expression: Choose the equivalent expression for $2^7 \times 2^3$ . $\newline$ $2^7 \times 2^3 = 2^{10}$ $\newline$ So, the equivalent expression is $2^{10}$ .

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