Simplify (3x^0y^4)(2x^2y)^3

$(3 x^{0} y^{4}) {(2 x^{2} y)}^{3}$

Step 1

Anything raised to $0$ is $1$ .

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

Step 2

Multiply $3$ by $1$ .

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

Step 3

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

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

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

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

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

Step 4

Multiply $y^{4}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

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

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

Add $3$ and $4$ .

$3 y^{7} (2^{3} {(x^{2})}^{3})$

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

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

$3 \cdot 8 y^{7} {(x^{2})}^{3}$

Step 7

Multiply $3$ by $8$ .

$24 y^{7} {(x^{2})}^{3}$

Step 8

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

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

$24 y^{7} x^{2 \cdot 3}$

Multiply $2$ by $3$ .

$24 y^{7} x^{6}$