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

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

Step 1

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

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

Step 2

Raise $2$ to the power of $3$ .

$3 x^{4} y (8 {(y^{2})}^{3})$

Step 3

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

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

$3 x^{4} y (8 y^{2 \cdot 3})$

Multiply $2$ by $3$ .

$3 x^{4} y (8 y^{6})$

Step 4

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

Move $y^{6}$ .

$3 x^{4} (y^{6} y) \cdot 8$

Multiply $y^{6}$ by $y$ .

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

$3 x^{4} (y^{6} y^{1}) \cdot 8$

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

$3 x^{4} y^{6 + 1} \cdot 8$

Add $6$ and $1$ .

$3 x^{4} y^{7} \cdot 8$

Step 5

Multiply $8$ by $3$ .

$24 x^{4} y^{7}$