Question

e following fraction in simplest form, only using ponents.
\frac{-5(r^3)^2}{5r^{10}}

Explanation:

Step1: Simplify the numerator's exponent

Use power rule: $(r^a)^b=r^{a \times b}$
$\frac{-5r^{3 \times 2}}{5r^{10}} = \frac{-5r^6}{5r^{10}}$

Step2: Simplify the constant coefficients

Divide the constants: $\frac{-5}{5}=-1$
$\frac{-1 \times r^6}{r^{10}}$

Step3: Simplify the variable terms

Use quotient rule: $\frac{r^a}{r^b}=r^{a-b}$
$-1 \times r^{6-10} = r^{-4} \times (-1)$

Answer:

$-r^{-4}$