Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

Multiply $2$ by $3$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

Apply the product rule to $2 x$ .

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

Step 2.3

Anything raised to $0$ is $1$ .

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

Step 2.4

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

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

Step 2.5

Anything raised to $0$ is $1$ .

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

Step 2.6

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

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Step 2.6.1

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

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

Step 2.6.2

Multiply $2$ by $0$ .

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

Step 2.7

Anything raised to $0$ is $1$ .

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

Step 2.8

Multiply $1$ by $1$ .

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

Step 3

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

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