Algebra Examples

$\frac{3 x^{3} y^{4} \cdot 6 x y^{- 5}}{{(3 x y)}^{2}}$

Step 1

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 1.1

Move $x$ .

$\frac{3 (x \cdot x^{3}) y^{4} \cdot (6 y^{- 5})}{{(3 x y)}^{2}}$

Step 1.2

Multiply $x$ by $x^{3}$ .

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Step 1.2.1

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

$\frac{3 (x^{1} x^{3}) y^{4} \cdot (6 y^{- 5})}{{(3 x y)}^{2}}$

Step 1.2.2

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

$\frac{3 x^{1 + 3} y^{4} \cdot (6 y^{- 5})}{{(3 x y)}^{2}}$

Step 1.3

Add $1$ and $3$ .

$\frac{3 x^{4} y^{4} \cdot (6 y^{- 5})}{{(3 x y)}^{2}}$

Step 2

Multiply $y^{4}$ by $y^{- 5}$ by adding the exponents.

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Step 2.1

Move $y^{- 5}$ .

$\frac{3 x^{4} (y^{- 5} y^{4}) \cdot 6}{{(3 x y)}^{2}}$

Step 2.2

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

$\frac{3 x^{4} y^{- 5 + 4} \cdot 6}{{(3 x y)}^{2}}$

Step 2.3

Add $- 5$ and $4$ .

$\frac{3 x^{4} y^{- 1} \cdot 6}{{(3 x y)}^{2}}$

Step 3

Simplify the expression.

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Step 3.1

Move $y^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 x^{4} \cdot 6}{{(3 x y)}^{2} y}$

Step 3.2

Multiply $6$ by $3$ .

$\frac{18 x^{4}}{{(3 x y)}^{2} y}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $3 x y$ .

$\frac{18 x^{4}}{{(3 x)}^{2} y^{2} y}$

Step 4.2

Combine exponents.

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Step 4.2.1

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

$\frac{18 x^{4}}{{(3 x)}^{2} (y^{1} y^{2})}$

Step 4.2.2

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

$\frac{18 x^{4}}{{(3 x)}^{2} y^{1 + 2}}$

Step 4.2.3

Add $1$ and $2$ .

$\frac{18 x^{4}}{{(3 x)}^{2} y^{3}}$

Step 4.3

Apply the product rule to $3 x$ .

$\frac{18 x^{4}}{3^{2} x^{2} y^{3}}$

Step 4.4

Raise $3$ to the power of $2$ .

$\frac{18 x^{4}}{9 x^{2} y^{3}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $18$ and $9$ .

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Step 5.1.1

Factor $9$ out of $18 x^{4}$ .

$\frac{9 (2 x^{4})}{9 x^{2} y^{3}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $9$ out of $9 x^{2} y^{3}$ .

$\frac{9 (2 x^{4})}{9 (x^{2} y^{3})}$

Step 5.1.2.2

Cancel the common factor.

$\frac{9 (2 x^{4})}{9 (x^{2} y^{3})}$

Step 5.1.2.3

Rewrite the expression.

$\frac{2 x^{4}}{x^{2} y^{3}}$

Step 5.2

Cancel the common factor of $x^{4}$ and $x^{2}$ .

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Step 5.2.1

Factor $x^{2}$ out of $2 x^{4}$ .

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

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $x^{2}$ out of $x^{2} y^{3}$ .

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

Step 5.2.2.2

Cancel the common factor.

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

Step 5.2.2.3

Rewrite the expression.

$\frac{2 x^{2}}{y^{3}}$