Write the Fraction in Simplest Form (2(r^5)^2)/(3r^6)

$\frac{2 {(r^{5})}^{2}}{3 r^{6}}$

Multiply the exponents in ${(r^{5})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 r^{5 \cdot 2}}{3 r^{6}}$

Multiply $5$ by $2$ .

$\frac{2 r^{10}}{3 r^{6}}$

Cancel the common factor of $r^{10}$ and $r^{6}$ .

Factor $r^{6}$ out of $2 r^{10}$ .

$\frac{r^{6} (2 r^{4})}{3 r^{6}}$

Cancel the common factors.

Factor $r^{6}$ out of $3 r^{6}$ .

$\frac{r^{6} (2 r^{4})}{r^{6} \cdot 3}$

Cancel the common factor.

$\frac{r^{6} (2 r^{4})}{r^{6} \cdot 3}$

Rewrite the expression.

$\frac{2 r^{4}}{3}$