Simplify (5xy^3)^2

${(5 x y^{3})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

${(5 x)}^{2} {(y^{3})}^{2}$

Apply the product rule to $5 x$ .

$5^{2} x^{2} {(y^{3})}^{2}$

Step 2

Raise $5$ to the power of $2$ .

$25 x^{2} {(y^{3})}^{2}$

Step 3

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

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

$25 x^{2} y^{3 \cdot 2}$

Multiply $3$ by $2$ .

$25 x^{2} y^{6}$