apply the property of Negative integer Exponents to find the numerical equivalent of 8^-3. The answer should not contian any exponent expression or decimals.

Question

8^-3 = _

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:

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

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

Now substituting back:

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

Thus, the final answer is:

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