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

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

Step 1

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $3$ and $2$ .

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

Step 2

Multiply $2$ by $2$ .

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

Step 3

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

Apply the product rule to $4 x^{4} y^{5}$ .

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

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

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

Step 4

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

$256 {(x^{4})}^{4} {(y^{5})}^{4}$

Step 5

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

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

$256 x^{4 \cdot 4} {(y^{5})}^{4}$

Multiply $4$ by $4$ .

$256 x^{16} {(y^{5})}^{4}$

Step 6

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

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

$256 x^{16} y^{5 \cdot 4}$

Multiply $5$ by $4$ .

$256 x^{16} y^{20}$