Question

Apply the Property of Negative Integer Exponents to solve 7 to the negative third power

Answer 1

To apply the property of negative integer exponents, we use the rule that states:

\[
a^{-n} = \frac{1}{a^n}
\]

For \(7^{-3}\), we can rewrite it as:

\[
7^{-3} = \frac{1}{7^3}
\]

Next, we need to calculate \(7^3\):

\[
7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343
\]

Now substituting back, we have:

\[
7^{-3} = \frac{1}{7^3} = \frac{1}{343}
\]

Thus, the value of \(7\) to the negative third power is:

\[
\boxed{\frac{1}{343}}
\]