Simplify (4x^4*2x^2y^9)^2

${(4 x^{4} \cdot 2 x^{2} y^{9})}^{2}$

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

${(4 (x^{2} x^{4}) \cdot (2 y^{9}))}^{2}$

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

${(4 x^{2 + 4} \cdot (2 y^{9}))}^{2}$

Add $2$ and $4$ .

${(4 x^{6} \cdot (2 y^{9}))}^{2}$

Rewrite using the commutative property of multiplication.

${(4 \cdot 2 x^{6} y^{9})}^{2}$

Multiply $4$ by $2$ .

${(8 x^{6} y^{9})}^{2}$

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

Apply the product rule to $8 x^{6} y^{9}$ .

${(8 x^{6})}^{2} {(y^{9})}^{2}$

Apply the product rule to $8 x^{6}$ .

$8^{2} {(x^{6})}^{2} {(y^{9})}^{2}$

Raise $8$ to the power of $2$ .

$64 {(x^{6})}^{2} {(y^{9})}^{2}$

Multiply the exponents in ${(x^{6})}^{2}$ .

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

$64 x^{6 \cdot 2} {(y^{9})}^{2}$

Multiply $6$ by $2$ .

$64 x^{12} {(y^{9})}^{2}$

Multiply the exponents in ${(y^{9})}^{2}$ .

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

$64 x^{12} y^{9 \cdot 2}$

Multiply $9$ by $2$ .

$64 x^{12} y^{18}$