Question

(\frac{r^{5}s^{7}}{r^{2}}=)

Explanation:

Step1: Apply exponent rule for division

When dividing terms with the same base, we subtract the exponents. For the base \( r \), we have \( \frac{r^5}{r^2} \), and the \( s^7 \) term remains as it is since there's no \( s \) in the denominator. The exponent rule is \( \frac{a^m}{a^n}=a^{m - n} \).
So, \( \frac{r^5}{r^2}=r^{5 - 2} \) and the \( s^7 \) stays.

Step2: Calculate the exponent of \( r \)

Calculate \( 5-2 = 3 \). So \( r^{5 - 2}=r^3 \).
Combining with \( s^7 \), we get \( r^3s^7 \).

Answer:

\( r^3s^7 \)