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

Question

options:

14^7 over 9^13

14^−7 ⋅ 9^13

1 over 9^13 ⋅ 14^−7

9^13 over 14^7

Answer 1

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

Starting with the original expression:

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

We can rewrite it as:

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

This can also be rearranged as:

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

Thus, the equivalent expression with only positive exponents is:

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

From the provided options, the correct answer is:

9^13 over 14^7.