Test Item 1

Which of the following is equal to [tex]2^{-3}[/tex]?

A. [tex]-2 \times -2 \times -2[/tex]

B. [tex]2 \times -3[/tex]

C. [tex]-3 \times -3[/tex]

D. [tex]\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}[/tex]



Answer :

To solve for [tex]\(2^{-3}\)[/tex]:

1. Recognize that a negative exponent indicates the reciprocal, as [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]. Thus, [tex]\(2^{-3} = \frac{1}{2^3}\)[/tex].

2. Compute [tex]\(2^3\)[/tex]:
[tex]\[ 2^3 = 2 \times 2 \times 2 = 8. \][/tex]

3. Therefore,
[tex]\[ 2^{-3} = \frac{1}{2^3} = \frac{1}{8}. \][/tex]

Let's examine the provided choices to see which one matches [tex]\( \frac{1}{8} \)[/tex]:

A) [tex]\(-2 \times -2 \times -2 = -8\)[/tex], which is incorrect because the result is negative and not the reciprocal of 8.

B) [tex]\(2 \times -3 = -6\)[/tex], which is incorrect because it's not related to the exponentiation operation.

C) [tex]\(-3 \times -3 = 9\)[/tex], which is incorrect because exponents are not involved in this operation, and the result is positive.

D) [tex]\(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\)[/tex]:
[tex]\[ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}, \][/tex]
[tex]\[ \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}, \][/tex]

This matches [tex]\(2^{-3} = \frac{1}{8}\)[/tex].

So, the correct choice is

D) [tex]\(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\)[/tex].