Simplify (2x^2y)^4(x^4y^5)^10

${(2 x^{2} y)}^{4} {(x^{4} y^{5})}^{10}$

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

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

${(2 x^{2})}^{4} y^{4} {(x^{4} y^{5})}^{10}$

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

$2^{4} {(x^{2})}^{4} y^{4} {(x^{4} y^{5})}^{10}$

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

$16 {(x^{2})}^{4} y^{4} {(x^{4} y^{5})}^{10}$

Multiply the exponents in ${(x^{2})}^{4}$ .

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

$16 x^{2 \cdot 4} y^{4} {(x^{4} y^{5})}^{10}$

Multiply $2$ by $4$ .

$16 x^{8} y^{4} {(x^{4} y^{5})}^{10}$

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

$16 x^{8} y^{4} ({(x^{4})}^{10} {(y^{5})}^{10})$

Multiply the exponents in ${(x^{4})}^{10}$ .

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

$16 x^{8} y^{4} (x^{4 \cdot 10} {(y^{5})}^{10})$

Multiply $4$ by $10$ .

$16 x^{8} y^{4} (x^{40} {(y^{5})}^{10})$

Multiply $x^{8}$ by $x^{40}$ by adding the exponents.

Move $x^{40}$ .

$16 (x^{40} x^{8}) y^{4} {(y^{5})}^{10}$

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

$16 x^{40 + 8} y^{4} {(y^{5})}^{10}$

Add $40$ and $8$ .

$16 x^{48} y^{4} {(y^{5})}^{10}$

Multiply the exponents in ${(y^{5})}^{10}$ .

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

$16 x^{48} y^{4} y^{5 \cdot 10}$

Multiply $5$ by $10$ .

$16 x^{48} y^{4} y^{50}$

Multiply $y^{4}$ by $y^{50}$ by adding the exponents.

Move $y^{50}$ .

$16 x^{48} (y^{50} y^{4})$

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

$16 x^{48} y^{50 + 4}$

Add $50$ and $4$ .

$16 x^{48} y^{54}$