Simplify (2x^3y^5)/(5(x^4y^2)^3)

$\frac{2 x^{3} y^{5}}{5 {(x^{4} y^{2})}^{3}}$

Step 1

Simplify the denominator.

Apply the product rule to $x^{4} y^{2}$ .

$\frac{2 x^{3} y^{5}}{5 {(x^{4})}^{3} {(y^{2})}^{3}}$

Multiply the exponents in ${(x^{4})}^{3}$ .

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

$\frac{2 x^{3} y^{5}}{5 x^{4 \cdot 3} {(y^{2})}^{3}}$

Multiply $4$ by $3$ .

$\frac{2 x^{3} y^{5}}{5 x^{12} {(y^{2})}^{3}}$

Multiply the exponents in ${(y^{2})}^{3}$ .

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

$\frac{2 x^{3} y^{5}}{5 x^{12} y^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{2 x^{3} y^{5}}{5 x^{12} y^{6}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{3}$ and $x^{12}$ .

Factor $x^{3}$ out of $2 x^{3} y^{5}$ .

$\frac{x^{3} (2 y^{5})}{5 x^{12} y^{6}}$

Cancel the common factors.

Factor $x^{3}$ out of $5 x^{12} y^{6}$ .

$\frac{x^{3} (2 y^{5})}{x^{3} (5 x^{9} y^{6})}$

Cancel the common factor.

$\frac{x^{3} (2 y^{5})}{x^{3} (5 x^{9} y^{6})}$

Rewrite the expression.

$\frac{2 y^{5}}{5 x^{9} y^{6}}$

Cancel the common factor of $y^{5}$ and $y^{6}$ .

Factor $y^{5}$ out of $2 y^{5}$ .

$\frac{y^{5} \cdot 2}{5 x^{9} y^{6}}$

Cancel the common factors.

Factor $y^{5}$ out of $5 x^{9} y^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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