To simplify the expression \( 15^{-7} - 29^{-5} \) using the Property of Negative Integer Exponents, we can rewrite it as follows:
- The property states that \( a^{-n} = \frac{1}{a^n} \). Therefore:
- \( 15^{-7} = \frac{1}{15^7} \)
- \( 29^{-5} = \frac{1}{29^5} \)
Thus, the original expression can be rewritten in terms of positive exponents:
\[ 15^{-7} - 29^{-5} = \frac{1}{15^7} - \frac{1}{29^5} \]
However, none of the options seem to match exactly with this form.
Let’s evaluate each of the response options to find the equivalent expression:
-
Response: \( \frac{15^{\frac{1}{7}}}{29^{\frac{1}{5}}} \)
- This doesn’t match the simplified form.
-
Response: \( \frac{1}{15^{7} \cdot 29^{5}} \)
- This is not equivalent since it does not accurately represent the subtraction of the two terms.
-
Response: \( \frac{15^{7}}{29^{5}} \)
- This does not match the simplified form either.
-
Response: \( \frac{29^{5}}{15^{7}} \)
- This is not equivalent to our original expression.
None of the given responses represent the correctly simplified form of \( 15^{-7} - 29^{-5} \).
If you were looking for just one choice that closely relates to negative exponents, you would ideally look for something like \( \frac{1}{15^7} - \frac{1}{29^5} \), but that's not present in your options.
Could you clarify if you are seeking something different in the response options?