Evaluate ((2y^5)^4)/(10y^15)

$\frac{{(2 y^{5})}^{4}}{10 y^{15}}$

Simplify the numerator.

Apply the product rule to $2 y^{5}$ .

$\frac{2^{4} {(y^{5})}^{4}}{10 y^{15}}$

Raise $2$ to the power of $4$ .

$\frac{16 {(y^{5})}^{4}}{10 y^{15}}$

Multiply the exponents in ${(y^{5})}^{4}$ .

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

$\frac{16 y^{5 \cdot 4}}{10 y^{15}}$

Multiply $5$ by $4$ .

$\frac{16 y^{20}}{10 y^{15}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $16$ and $10$ .

Factor $2$ out of $16 y^{20}$ .

$\frac{2 (8 y^{20})}{10 y^{15}}$

Cancel the common factors.

Factor $2$ out of $10 y^{15}$ .

$\frac{2 (8 y^{20})}{2 (5 y^{15})}$

Cancel the common factor.

$\frac{2 (8 y^{20})}{2 (5 y^{15})}$

Rewrite the expression.

$\frac{8 y^{20}}{5 y^{15}}$

Cancel the common factor of $y^{20}$ and $y^{15}$ .

Factor $y^{15}$ out of $8 y^{20}$ .

$\frac{y^{15} (8 y^{5})}{5 y^{15}}$

Cancel the common factors.

Factor $y^{15}$ out of $5 y^{15}$ .

$\frac{y^{15} (8 y^{5})}{y^{15} \cdot 5}$

Cancel the common factor.

$\frac{y^{15} (8 y^{5})}{y^{15} \cdot 5}$

Rewrite the expression.

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