Question Which of the following is an equivalent expression to 14^−7/9^−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?

1 answer

To rewrite the expression \( 14^{-7} / 9^{-13} \) with only positive exponents, we can apply the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Using this property, we can rewrite the expression as follows:

\[ 14^{-7} / 9^{-13} = \frac{1}{14^7} \cdot \frac{1}{9^{-13}} = \frac{1}{14^7} \cdot 9^{13} \]

Next, we multiply the two fractions together:

\[ = \frac{9^{13}}{14^7} \]

Thus, an equivalent expression to \( 14^{-7} / 9^{-13} \) with only positive exponents is:

\[ \frac{9^{13}}{14^7} \]