Which of the following is an equivalent expression to 14−79−13

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 \( 14^{-7} \cdot 9^{13} \) into an equivalent expression with only positive exponents, we can apply the Property of Negative Integer Exponents. The property states that \( a^{-n} = \frac{1}{a^n} \).

Using this property, we can rewrite \( 14^{-7} \) as:

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

So, the expression \( 14^{-7} \cdot 9^{13} \) can be rewritten as:

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

Thus, the equivalent expression with only positive exponents is:

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

Looking at the provided responses, the equivalent expression is:

\[ \text{Start Fraction } 9^{13} \text{ over } 14^{7} \text{ End Fraction} \]

So, the correct answer is:

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