Which of the following is an equivalent expression to 14−79−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)

Question

Responses

147913
Start Fraction 14 superscript 7 baseline over 9 superscript 13 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

1913 ⋅14−7
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction

Answer 1

To rewrite the expression \( 14^{-7} \cdot 9^{-13} \) with positive exponents, we use the Property of Negative Integer Exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Applying this property to the expression:

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

So, we can write:

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

Alternatively, we can express it as:

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

Thus, the equivalent expression in terms of positive exponents would be:

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

Therefore, the correct response that denotes this equivalent expression is:

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

This matches with the option:

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