Question

simplify. express your answer using positive exponents.
$\frac{3rs}{3rs^{7}}$

Explanation:

Step1: Cancel out common factors

Cancel out the common factor 3 in the numerator and denominator: $\frac{3rs}{3rs^{7}}=\frac{rs}{rs^{7}}$

Step2: Use exponent - division rule

According to the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$, for the $r$ terms $\frac{r}{r}=r^{1 - 1}=r^{0}=1$, and for the $s$ terms $\frac{s}{s^{7}}=s^{1-7}=s^{- 6}$. Since we want positive exponents, $\frac{1}{s^{6}}$.

Answer:

$\frac{1}{s^{6}}$