Question

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) Responses 14−7⋅913 14 superscript negative 7 baseline times 9 superscript 13 baseline 1913 ⋅14−7 Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction 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

Answer 1

To express \( 14^{-7} \cdot 9^{13} \) using only positive exponents, we can apply the Property of Negative Integer Exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

So, for \( 14^{-7} \): \[ 14^{-7} = \frac{1}{14^{7}} \]

Thus, our expression becomes: \[ 14^{-7} \cdot 9^{13} = \frac{1}{14^{7}} \cdot 9^{13} = \frac{9^{13}}{14^{7}} \]

Now let's review the response options to find the equivalent expression with only positive exponents:

1. \( 14^{-7} \cdot 9^{13} \) - Not in positive form.
2. \( 14^{-7} \cdot 9^{13} \) - Not in positive form (same as option 1).
3. \( \frac{1}{9^{13} \cdot 14^{-7}} \) - Also not correct because \( 14^{-7} \) is still negative.
4. \( \frac{9^{13}}{14^{7}} \) - This is in positive exponent form.
5. \( \frac{14^{7}}{9^{13}} \) - Not equivalent since the numerator and denominator are switched.

Thus, the correct response that is equivalent to \( 14^{-7} \cdot 9^{13} \) with only positive exponents is: \[ \frac{9^{13}}{14^{7}} \]