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

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

Step 1

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

Apply the product rule to $2 x^{3} y^{5}$ .

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

Apply the product rule to $2 x^{3}$ .

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

Step 2

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

$16 {(x^{3})}^{4} {(y^{5})}^{4}$

Step 3

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

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

$16 x^{3 \cdot 4} {(y^{5})}^{4}$

Multiply $3$ by $4$ .

$16 x^{12} {(y^{5})}^{4}$

Step 4

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

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

$16 x^{12} y^{5 \cdot 4}$

Multiply $5$ by $4$ .

$16 x^{12} y^{20}$