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

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

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

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

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

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

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

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

Move $y^{3}$ .

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

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

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

Add $3$ and $3$ .

$3^{3} {(x^{2})}^{3} y^{6} {(2 x y^{4})}^{2}$

Raise $3$ to the power of $3$ .

$27 {(x^{2})}^{3} y^{6} {(2 x y^{4})}^{2}$

Multiply the exponents in ${(x^{2})}^{3}$ .

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

$27 x^{2 \cdot 3} y^{6} {(2 x y^{4})}^{2}$

Multiply $2$ by $3$ .

$27 x^{6} y^{6} {(2 x y^{4})}^{2}$

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

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

$27 x^{6} y^{6} ({(2 x)}^{2} {(y^{4})}^{2})$

Apply the product rule to $2 x$ .

$27 x^{6} y^{6} (2^{2} x^{2} {(y^{4})}^{2})$

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$27 (x^{2} x^{6}) y^{6} (2^{2} {(y^{4})}^{2})$

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

$27 x^{2 + 6} y^{6} (2^{2} {(y^{4})}^{2})$

Add $2$ and $6$ .

$27 x^{8} y^{6} (2^{2} {(y^{4})}^{2})$

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

$27 x^{8} y^{6} (4 {(y^{4})}^{2})$

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

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

$27 x^{8} y^{6} (4 y^{4 \cdot 2})$

Multiply $4$ by $2$ .

$27 x^{8} y^{6} (4 y^{8})$

Multiply $y^{6}$ by $y^{8}$ by adding the exponents.

Move $y^{8}$ .

$27 x^{8} (y^{8} y^{6}) \cdot 4$

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

$27 x^{8} y^{8 + 6} \cdot 4$

Add $8$ and $6$ .

$27 x^{8} y^{14} \cdot 4$

Multiply $4$ by $27$ .

$108 x^{8} y^{14}$

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

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