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 point)

Question

Responses

14^−7⋅9^13
14 superscript negative 7 baseline times 9 superscript 13 baseline

9^13/14^7
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction

1/9^13 ⋅14^−7
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction

14^7/9^13

Answer 1

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

Starting with the original expression:

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

We can rewrite it using positive exponents:

1. For \( 14^{-7} \), apply the negative exponent property:

\[ 14^{-7} = \frac{1}{14^7} \]

2. For \( 9^{-13} \), apply the negative exponent property:

\[ 9^{-13} = \frac{1}{9^{13}} \]

Thus, the expression becomes:

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

This simplifies to:

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

Thus, the final expression with only positive exponents is:

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

Therefore, the equivalent expression from your options is:

9^13/14^7