Simplify (5y)/((3y^5)^2)

$\frac{5 y}{{(3 y^{5})}^{2}}$

Step 1

Simplify the denominator.

Apply the product rule to $3 y^{5}$ .

$\frac{5 y}{3^{2} {(y^{5})}^{2}}$

Raise $3$ to the power of $2$ .

$\frac{5 y}{9 {(y^{5})}^{2}}$

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

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

$\frac{5 y}{9 y^{5 \cdot 2}}$

Multiply $5$ by $2$ .

$\frac{5 y}{9 y^{10}}$

Step 2

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

Factor $y$ out of $5 y$ .

$\frac{y \cdot 5}{9 y^{10}}$

Cancel the common factors.

Factor $y$ out of $9 y^{10}$ .

$\frac{y \cdot 5}{y (9 y^{9})}$

Cancel the common factor.

$\frac{y \cdot 5}{y (9 y^{9})}$

Rewrite the expression.

$\frac{5}{9 y^{9}}$