Simplify ((3x^2y)^3)/((2xy^2)^0)

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

Simplify the numerator.

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

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

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

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

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

$\frac{27 {(x^{2})}^{3} y^{3}}{{(2 x y^{2})}^{0}}$

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

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

$\frac{27 x^{2 \cdot 3} y^{3}}{{(2 x y^{2})}^{0}}$

Multiply $2$ by $3$ .

$\frac{27 x^{6} y^{3}}{{(2 x y^{2})}^{0}}$

Simplify the denominator.

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

$\frac{27 x^{6} y^{3}}{{(2 x)}^{0} {(y^{2})}^{0}}$

Apply the product rule to $2 x$ .

$\frac{27 x^{6} y^{3}}{2^{0} x^{0} {(y^{2})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{27 x^{6} y^{3}}{1 x^{0} {(y^{2})}^{0}}$

Multiply $x^{0}$ by $1$ .

$\frac{27 x^{6} y^{3}}{x^{0} {(y^{2})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{27 x^{6} y^{3}}{1 {(y^{2})}^{0}}$

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

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

$\frac{27 x^{6} y^{3}}{1 y^{2 \cdot 0}}$

Multiply $2$ by $0$ .

$\frac{27 x^{6} y^{3}}{1 y^{0}}$

Anything raised to $0$ is $1$ .

$\frac{27 x^{6} y^{3}}{1 \cdot 1}$

Multiply $1$ by $1$ .

$\frac{27 x^{6} y^{3}}{1}$

Divide $27 x^{6} y^{3}$ by $1$ .

$27 x^{6} y^{3}$