Negative Integer Exponents Quick Check

Question

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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

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

Answer 1

To convert the expression \( 14^{-7} \cdot 9^{13} \) into an equivalent expression with only positive exponents, we apply the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Here's the breakdown:

1. The term \( 14^{-7} \) can be rewritten as \( \frac{1}{14^7} \).
2. The term \( 9^{13} \) is already in positive exponent form.

Combining these, we get:

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

This can be further simplified to:

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

From the provided options, this matches the second option:

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

Therefore, the equivalent expression with only positive exponents is:

\( 913147 \) (Starting fraction \( 9^{13} \) over \( 14^{7} \)).