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

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

14−7⋅913
14 superscript negative 7 baseline times 9 superscript 13 baseline

913147
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction

14^7/9^13

Answer 1

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

Starting with:

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

We can apply the negative exponent rule:

1. Rewrite \( 14^{-7} \) as \( \frac{1}{14^7} \).
2. Rewrite \( 9^{-13} \) as \( \frac{1}{9^{13}} \).

Thus:

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

When dividing by a fraction, it is equivalent to multiplying by the reciprocal:

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

Therefore, an equivalent expression using only positive exponents is:

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

In the provided options, this corresponds to:

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

So the correct answer is:

\(\frac{9^{13}}{14^{7}}\)