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

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

Step 1

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

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$4 (x^{2} x^{1}) y (2 y) {(3 x y)}^{3}$

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

$4 x^{2 + 1} y (2 y) {(3 x y)}^{3}$

Add $2$ and $1$ .

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

Step 2

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Step 3

Multiply $2$ by $4$ .

$8 x^{3} y^{2} {(3 x y)}^{3}$

Step 4

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

Apply the product rule to $3 x y$ .

$8 x^{3} y^{2} ({(3 x)}^{3} y^{3})$

Apply the product rule to $3 x$ .

$8 x^{3} y^{2} (3^{3} x^{3} y^{3})$

Step 5

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

Move $x^{3}$ .

$8 (x^{3} x^{3}) y^{2} (3^{3} y^{3})$

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

$8 x^{3 + 3} y^{2} (3^{3} y^{3})$

Add $3$ and $3$ .

$8 x^{6} y^{2} (3^{3} y^{3})$

Step 6

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

Move $y^{3}$ .

$8 x^{6} (y^{3} y^{2}) \cdot 3^{3}$

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

$8 x^{6} y^{3 + 2} \cdot 3^{3}$

Add $3$ and $2$ .

$8 x^{6} y^{5} \cdot 3^{3}$

Step 7

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

$8 x^{6} y^{5} \cdot 27$

Step 8

Multiply $27$ by $8$ .

$216 x^{6} y^{5}$

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

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