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.

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 \( 8^{-3} \):

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

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

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

Calculating step by step:

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

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

Now substituting this back into our expression gives:

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

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

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