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

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

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

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

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

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

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

Anything raised to $0$ is $1$ .

$4 x (1 {(x^{2})}^{0} y^{0})$

Multiply ${(x^{2})}^{0}$ by $1$ .

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

Multiply the exponents in ${(x^{2})}^{0}$ .

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

$4 x (x^{2 \cdot 0} y^{0})$

Multiply $2$ by $0$ .

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

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

Move $x^{0}$ .

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

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

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

$4 (x^{0} x^{1}) y^{0}$

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

$4 x^{0 + 1} y^{0}$

Add $0$ and $1$ .

$4 x^{1} y^{0}$

Simplify $4 x^{1} y^{0}$ .

$4 x$