To find the numerical equivalent of \( 8^{-3} \) using the property of negative integer exponents, we can use the rule:
\[ a^{-n} = \frac{1}{a^n} \]
In this case, 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:
\[ 8 \times 8 = 64 \] \[ 64 \times 8 = 512 \]
So, \( 8^3 = 512 \). Therefore, we can substitute this back into the equation:
\[ 8^{-3} = \frac{1}{512} \]
Thus, the numerical equivalent of \( 8^{-3} \) is
\[ \frac{1}{512} \]
This answer does not contain any exponent expressions or decimals.