Question

perform the indicated operations. write the answer using only positive exponents. $\frac{8r^{-6}}{12r^{-12}}$ $\frac{8r^{-6}}{12r^{-12}}=square$ (simplify your answer. use integers or fractions for any numbers in the expression)

Explanation:

Step1: Simplify the coefficient

Simplify $\frac{8}{12}$ to $\frac{2}{3}$.
$\frac{8}{12}=\frac{2}{3}$

Step2: Use exponent - rule for division

According to the rule $\frac{a^m}{a^n}=a^{m - n}$, for $r^{-6}$ divided by $r^{-12}$, we have $r^{-6-(-12)}=r^{-6 + 12}=r^{6}$.
$\frac{r^{-6}}{r^{-12}}=r^{-6-(-12)}=r^{6}$

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable - part.
$\frac{2}{3}r^{6}$

Answer:

$\frac{2r^{6}}{3}$