Write the Fraction in Simplest Form (3(r^2)^4)/(15r^8)

$\frac{3 {(r^{2})}^{4}}{15 r^{8}}$

Step 1

Cancel the common factor of $3$ and $15$ .

Factor $3$ out of $3 {(r^{2})}^{4}$ .

$\frac{3 ({(r^{2})}^{4})}{15 r^{8}}$

Cancel the common factors.

Factor $3$ out of $15 r^{8}$ .

$\frac{3 ({(r^{2})}^{4})}{3 (5 r^{8})}$

Cancel the common factor.

$\frac{3 {(r^{2})}^{4}}{3 (5 r^{8})}$

Rewrite the expression.

$\frac{{(r^{2})}^{4}}{5 r^{8}}$

Step 2

Multiply the exponents in ${(r^{2})}^{4}$ .

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

$\frac{r^{2 \cdot 4}}{5 r^{8}}$

Multiply $2$ by $4$ .

$\frac{r^{8}}{5 r^{8}}$

Step 3

Cancel the common factor of $r^{8}$ .

Cancel the common factor.

$\frac{r^{8}}{5 r^{8}}$

Rewrite the expression.

$\frac{1}{5}$