Simplify 3x^32x^2y4x^2y

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

Step 1

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

Move $x^{2}$ .

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

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

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

Add $2$ and $3$ .

$3 x^{5} \cdot (2 y) \cdot (4 x^{2} y)$

Step 2

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$3 (x^{2} x^{5}) \cdot (2 y) \cdot (4 y)$

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

$3 x^{2 + 5} \cdot (2 y) \cdot (4 y)$

Add $2$ and $5$ .

$3 x^{7} \cdot (2 y) \cdot (4 y)$

Step 3

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

Move $y$ .

$3 x^{7} \cdot (2 (y \cdot y)) \cdot 4$

Multiply $y$ by $y$ .

$3 x^{7} \cdot (2 y^{2}) \cdot 4$

Step 4

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x^{7} y^{2} \cdot 4$

Step 5

Multiply $3$ by $2$ .

$6 x^{7} y^{2} \cdot 4$

Step 6

Multiply $4$ by $6$ .

$24 x^{7} y^{2}$

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