To find the numerical equivalent of \( 8^{-3} \) using the property of negative integer exponents, we can use the following property:
\[ a^{-n} = \frac{1}{a^n} \]
Applying this property to \( 8^{-3} \):
\[ 8^{-3} = \frac{1}{8^3} \]
Now, we need to calculate \( 8^3 \), which means \( 8 \times 8 \times 8 \).
Calculating step by step:
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First, calculate \( 8 \times 8 \): \[ 8 \times 8 = 64 \]
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Next, multiply the result by \( 8 \): \[ 64 \times 8 = 512 \]
Thus, \( 8^3 = 512 \).
Now substituting this back into our expression:
\[ 8^{-3} = \frac{1}{8^3} = \frac{1}{512} \]
Therefore, the numerical equivalent of \( 8^{-3} \) is
\[ \boxed{\frac{1}{512}} \]