Which of the following is an equivalent expression to 15−729−5 generated by the Property of Negative Integer Exponents?(1 point)

Question

Responses

295157
Start Fraction 29 superscript 5 baseline over 15 superscript 7 baseline End Fraction

157295
Start Fraction 15 superscript 7 baseline over 29 superscript 5 baseline End Fraction

1157. 295
Start Fraction 1 over 15 superscript 7 baseline times 29 superscript 5 baseline End Fraction

15172915

Answer 1

To simplify the expression \(15^{-7} \cdot 29^{-5}\) using the Property of Negative Integer Exponents, we can rewrite it as follows:

\[ 15^{-7} = \frac{1}{15^7} \quad \text{and} \quad 29^{-5} = \frac{1}{29^5} \]

Thus,

\[ 15^{-7} \cdot 29^{-5} = \frac{1}{15^7} \cdot \frac{1}{29^5} = \frac{1}{15^7 \cdot 29^5} \]

This means we can write it as:

\[ \frac{1}{15^7 \cdot 29^5} = \frac{1}{15^7 \cdot 29^5} \quad \text{or} \quad \frac{1}{15^7 \cdot 29^5} \]

Looking at the options you provided:

• \( \frac{29^5}{15^7} \) (not equivalent)
• \( \frac{15^7}{29^5} \) (not equivalent)
• \( \frac{1}{15^7 \cdot 29^5} \) (this is equivalent)
• \( 15 \cdot 29^{15} \) (not equivalent)

The equivalent expression is:

\[ \frac{1}{15^7 \cdot 29^5} \]

So the correct answer is:

\( \frac{1}{15^7 \cdot 29^5} \).

Answer 2

So whats the answer?

Answer 3

The equivalent expression to \(15^{-7} \cdot 29^{-5}\) is:

\( \frac{1}{15^7 \cdot 29^5} \).

This corresponds to the option:

\( \frac{1}{15^7 \cdot 29^5} \).