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:

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