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

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

2 \times 2^2

?

\newline

Choices:

\newline

(A)

\frac{1}{2^3}

\newline

(B)

2^3

\newline

(C)

2^2

\newline

(D)

\frac{1}{2^2}

Identify Base and Exponents: Identify the base and the exponents. $\newline$ In the expression $2 \times 2^2$ , $2$ is the base raised to the exponents $1$ and $2$ respectively. $\newline$ Base: $2$ $\newline$ Exponents: $1$ , $2$
Rewrite Expression as Single Power: Given expression: $2^1 \times 2^2$ $\newline$ Rewrite this expression as a single power of $2$ . $\newline$ When we multiply powers with the same base, we add the exponents. $\newline$ $2^1 \times 2^2$ $\newline$ $= 2^{1+2}$ $\newline$ $= 2^3$
Simplify $2^3$ : Simplify $2^3$ . $\$2^3 = 2 \times 2 \times 2$ \) $= 4 \times 2\$$ $= 8$ \)
Choose Equivalent Expression: Choose the equivalent expression for $2 \times 2^2$ . $\newline$ $2 \times 2^2 = 2^3$ $\newline$ $2 \times 2^2$ is equivalent to $8$ , which is the same as $2^3$ .

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