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.

1 answer

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.