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

9/131^47

14^7/9^13

14−7⋅9^13 14

1/9^13 ⋅14−7

Answer 1

To simplify the expression \( 14^{-7} - 9^{-13} \) using the property of negative integer exponents, we can rewrite it in terms of positive exponents.

The property states that

\[ a^{-n} = \frac{1}{a^n}. \]

Applying this property to our expression:

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

Thus, we have:

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

However, the question specifically asks for an equivalent expression that uses only positive exponents.

Given the options:

1. \( \frac{9}{13} \cdot 1^{47} \)
2. \( \frac{14^7}{9^{13}} \)
3. \( 14^{-7} \cdot 9^{13} \cdot 14 \)
4. \( \frac{1}{9^{13}} \cdot 14^{-7} \)

The second option, \( \frac{14^7}{9^{13}} \), correctly shows \( 14^{-7} \) rewritten as \( \frac{1}{14^7} \) and does not include any negative exponents anymore. Hence, this is our equivalent expression.

So the equivalent expression to \( 14^{-7} - 9^{-13} \) with only positive exponents would be:

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