Algebra Examples

$\frac{{(4 x^{5} y^{2})}^{0} {(3 x^{2} y^{3})}^{3}}{{(x^{3} y)}^{3}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $4 x^{5} y^{2}$ .

$\frac{{(4 x^{5})}^{0} {(y^{2})}^{0} {(3 x^{2} y^{3})}^{3}}{{(x^{3} y)}^{3}}$

Step 1.2

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

$\frac{{(4 x^{5})}^{0} {(y^{2})}^{0} {(3 x^{2})}^{3} {(y^{3})}^{3}}{{(x^{3} y)}^{3}}$

Step 1.3

Apply the product rule to $4 x^{5}$ .

$\frac{4^{0} {(x^{5})}^{0} {(y^{2})}^{0} {(3 x^{2})}^{3} {(y^{3})}^{3}}{{(x^{3} y)}^{3}}$

Step 1.4

Anything raised to $0$ is $1$ .

$\frac{1 {(x^{5})}^{0} {(y^{2})}^{0} {(3 x^{2})}^{3} {(y^{3})}^{3}}{{(x^{3} y)}^{3}}$

Step 1.5

Multiply ${(x^{5})}^{0}$ by $1$ .

$\frac{{(x^{5})}^{0} {(y^{2})}^{0} {(3 x^{2})}^{3} {(y^{3})}^{3}}{{(x^{3} y)}^{3}}$

Step 1.6

Multiply the exponents in ${(x^{5})}^{0}$ .

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Step 1.6.1

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

$\frac{x^{5 \cdot 0} {(y^{2})}^{0} {(3 x^{2})}^{3} {(y^{3})}^{3}}{{(x^{3} y)}^{3}}$

Step 1.6.2

Multiply $5$ by $0$ .

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

Step 1.7

Anything raised to $0$ is $1$ .

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

Step 1.8

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

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Step 1.8.1

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

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

Step 1.8.2

Multiply $2$ by $0$ .

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

Step 1.9

Anything raised to $0$ is $1$ .

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

Step 1.10

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

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

Step 1.11

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

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

Step 1.12

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

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Step 1.12.1

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

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

Step 1.12.2

Multiply $2$ by $3$ .

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

Step 1.13

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

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Step 1.13.1

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

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

Step 1.13.2

Multiply $3$ by $3$ .

$\frac{1 \cdot 1 (27 x^{6}) y^{9}}{{(x^{3} y)}^{3}}$

$\frac{1 \cdot 1 \cdot 27 x^{6} y^{9}}{{(x^{3} y)}^{3}}$

Step 1.14

Combine exponents.

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Step 1.14.1

Multiply $1$ by $1$ .

$\frac{1 \cdot 27 x^{6} y^{9}}{{(x^{3} y)}^{3}}$

Step 1.14.2

Multiply $27$ by $1$ .

$\frac{27 x^{6} y^{9}}{{(x^{3} y)}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{27 x^{6} y^{9}}{{(x^{3})}^{3} y^{3}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{27 x^{6} y^{9}}{x^{3 \cdot 3} y^{3}}$

Step 2.2.2

Multiply $3$ by $3$ .

$\frac{27 x^{6} y^{9}}{x^{9} y^{3}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x^{6}$ and $x^{9}$ .

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Step 3.1.1

Factor $x^{6}$ out of $27 x^{6} y^{9}$ .

$\frac{x^{6} (27 y^{9})}{x^{9} y^{3}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $x^{6}$ out of $x^{9} y^{3}$ .

$\frac{x^{6} (27 y^{9})}{x^{6} (x^{3} y^{3})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{x^{6} (27 y^{9})}{x^{6} (x^{3} y^{3})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{27 y^{9}}{x^{3} y^{3}}$

Step 3.2

Cancel the common factor of $y^{9}$ and $y^{3}$ .

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Step 3.2.1

Factor $y^{3}$ out of $27 y^{9}$ .

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

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $y^{3}$ out of $x^{3} y^{3}$ .

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

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