Question

Apply the Property of Negative Integer Exponents to find the numerical equivalent of 8−3
. The answer should not contain any exponent expression or decimals.

Show your work.

(1 point)
8−3=

Answer 1

To evaluate \( 8^{-3} \) using the property of negative integer exponents, we can use the rule that states:

\[
a^{-n} = \frac{1}{a^n}
\]

Applying this to \( 8^{-3} \):

\[
8^{-3} = \frac{1}{8^3}
\]

Now, we need to calculate \( 8^3 \):

\[
8^3 = 8 \times 8 \times 8
\]

Calculating step-by-step:

1. First, calculate \( 8 \times 8 \):
\[
8 \times 8 = 64
\]

2. Next, multiply that result by \( 8 \):
\[
64 \times 8 = 512
\]

Now, we can substitute this value back into our earlier expression:

\[
8^{-3} = \frac{1}{8^3} = \frac{1}{512}
\]

Thus, the numerical equivalent of \( 8^{-3} \) is:

\[
\boxed{\frac{1}{512}}
\]