Which of the following is an equivalent expression to 14^−7/9^−13

Question

with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses

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

 147913
  Start Fraction 14 superscript 7 baseline over 9 superscript 13 baseline End Fraction

1913 ⋅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
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Answer 1

To convert the expression \( 14^{-7}/9^{-13} \) into an equivalent expression with only positive exponents, we will apply the property of negative exponents:

1. Recall that \( a^{-n} = \frac{1}{a^n} \), and that \( \frac{a^{-m}}{b^{-n}} = \frac{b^n}{a^m} \).

Applying this property to our expression \( 14^{-7}/9^{-13} \):

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

This can also be expressed as:

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

Thus, the equivalent expression with only positive exponents is:

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

Now, looking at the provided responses, the correct equivalent expression is:

Start Fraction \( 9^{13} \) over \( 14^{7} \) End Fraction

So the answer is:

Start Fraction \( 9^{13} \) over \( 14^{7} \) End Fraction