Which expression is equivalent to 2^7 * 2^6? Choices: (A)2^13 (B)1/2^42 (C)1/2^13 (D)2^42

Identify Base and Exponents: Identify the base and the exponents. In 2^7 and 2^6, 2 is the base raised to the exponents 7 and 6 respectively. Base: 2 Exponents: 7, 6Rewrite Expression: Given expression: 2^7 * 2^6 Rewrite this expression as a single power of 2. When we multiply powers with the same base, we add the exponents. 2^7 * 2^6 = 2^(7+6) = 2^13Choose Equivalent Expression: Choose the equivalent expression for 2^7 * 2^6. 2^7 * 2^6 = 2^13 The equivalent expression is 2^13, which corresponds to choice (A).

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Math Problems

Grade 8

Identify equivalent expressions involving exponents I

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Q. Which expression is equivalent to

2^7 \times 2^6

\newline

Choices:

\newline

(A)

2^{13}

\newline

(B)

\frac{1}{2^{42}}

\newline

(C)

\frac{1}{2^{13}}

\newline

(D)

2^{42}

Identify Base and Exponents: Identify the base and the exponents. $\newline$ In $2^7$ and $2^6$ , $2$ is the base raised to the exponents $7$ and $6$ respectively. $\newline$ Base: $2$ $\newline$ Exponents: $7$ , $6$
Rewrite Expression: Given expression: $2^7 \times 2^6$ $\newline$ Rewrite this expression as a single power of $2$ . $\newline$ When we multiply powers with the same base, we add the exponents. $\newline$ $2^7 \times 2^6$ $\newline$ $= 2^{7+6}$ $\newline$ $= 2^{13}$
Choose Equivalent Expression: Choose the equivalent expression for $2^7 \times 2^6$ . $\newline$ $2^7 \times 2^6 = 2^{13}$ $\newline$ The equivalent expression is $2^{13}$ , which corresponds to choice (A).