Question

Apply the Property of Negative Integer Exponents to find the numerical equivalent of 8to the−3 power. The answer should not contain any exponent expression or decimals. Show your work. (1 point) 8to the−3power=

Answer 1

To find the numerical equivalent of \( 8^{-3} \), we can use the Property of Negative Integer Exponents, which states that:

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

Applying this property to \( 8^{-3} \), we have:

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

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

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

Calculating step-by-step:

1. \( 8 \times 8 = 64 \)
2. \( 64 \times 8 = 512 \)

So, \( 8^3 = 512 \).

Now we substitute this value back into our expression:

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

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

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