Apply the Property of Negative Integer Exponents to solve 7^-3 . The answer should not contain any exponent expression or decimals.

Answer 1

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

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

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

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

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

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

Calculating step-by-step:

1. \(7 \times 7 = 49\)
2. \(49 \times 7 = 343\)

So, \(7^3 = 343\). Therefore, we have:

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

Thus, the final answer is:

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