Simplify (x^2y^4)^5

${(x^{2} y^{4})}^{5}$

Step 1

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

${(x^{2})}^{5} {(y^{4})}^{5}$

Step 2

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

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

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

Multiply $2$ by $5$ .

$x^{10} {(y^{4})}^{5}$

Step 3

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

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

$x^{10} y^{4 \cdot 5}$

Multiply $4$ by $5$ .

$x^{10} y^{20}$