Simplify (2xy^3)^0(3xy)

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

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

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

Apply the product rule to $2 x$ .

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

Step 3

Multiply $x^{0}$ by $x$ by adding the exponents.

Move $x$ .

$3 (2^{0} (x \cdot x^{0}) {(y^{3})}^{0}) y$

Multiply $x$ by $x^{0}$ .

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

$3 (2^{0} (x^{1} x^{0}) {(y^{3})}^{0}) y$

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

$3 (2^{0} x^{1 + 0} {(y^{3})}^{0}) y$

Add $1$ and $0$ .

$3 (2^{0} x^{1} {(y^{3})}^{0}) y$

Step 4

Simplify $3 (2^{0} x^{1} {(y^{3})}^{0}) y$ .

$3 x y$