Write the Fraction in Simplest Form (4(s^4)^4)/(20s^8)

$\frac{4 {(s^{4})}^{4}}{20 s^{8}}$

Step 1

Cancel the common factor of $4$ and $20$ .

Factor $4$ out of $4 {(s^{4})}^{4}$ .

$\frac{4 ({(s^{4})}^{4})}{20 s^{8}}$

Cancel the common factors.

Factor $4$ out of $20 s^{8}$ .

$\frac{4 ({(s^{4})}^{4})}{4 (5 s^{8})}$

Cancel the common factor.

$\frac{4 {(s^{4})}^{4}}{4 (5 s^{8})}$

Rewrite the expression.

$\frac{{(s^{4})}^{4}}{5 s^{8}}$

Step 2

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

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

$\frac{s^{4 \cdot 4}}{5 s^{8}}$

Multiply $4$ by $4$ .

$\frac{s^{16}}{5 s^{8}}$

Step 3

Cancel the common factor of $s^{16}$ and $s^{8}$ .

Factor $s^{8}$ out of $s^{16}$ .

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

Cancel the common factors.

Factor $s^{8}$ out of $5 s^{8}$ .

$\frac{s^{8} s^{8}}{s^{8} \cdot 5}$

Cancel the common factor.

$\frac{s^{8} s^{8}}{s^{8} \cdot 5}$

Rewrite the expression.

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