Algebra Examples

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

Step 1

Multiply $x^{- 3}$ by $x^{- 4}$ by adding the exponents.

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Step 1.1

Move $x^{- 4}$ .

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

Step 1.2

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

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

Step 1.3

Subtract $3$ from $- 4$ .

$\frac{3 x^{- 7} y^{2} \cdot y^{- 4}}{3 x y^{2} \cdot (3 y x^{- 1})}$

Step 2

Multiply $y^{2}$ by $y^{- 4}$ by adding the exponents.

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Step 2.1

Move $y^{- 4}$ .

$\frac{3 x^{- 7} (y^{- 4} y^{2})}{3 x y^{2} \cdot (3 y x^{- 1})}$

Step 2.2

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

$\frac{3 x^{- 7} y^{- 4 + 2}}{3 x y^{2} \cdot (3 y x^{- 1})}$

Step 2.3

Add $- 4$ and $2$ .

$\frac{3 x^{- 7} y^{- 2}}{3 x y^{2} \cdot (3 y x^{- 1})}$

Step 3

Multiply $x$ by $x^{- 1}$ by adding the exponents.

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Step 3.1

Move $x^{- 1}$ .

$\frac{3 x^{- 7} y^{- 2}}{3 (x^{- 1} x) y^{2} \cdot (3 y)}$

Step 3.2

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

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Step 3.2.1

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

$\frac{3 x^{- 7} y^{- 2}}{3 (x^{- 1} x^{1}) y^{2} \cdot (3 y)}$

Step 3.2.2

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

$\frac{3 x^{- 7} y^{- 2}}{3 x^{- 1 + 1} y^{2} \cdot (3 y)}$

Step 3.3

Add $- 1$ and $1$ .

$\frac{3 x^{- 7} y^{- 2}}{3 x^{0} y^{2} \cdot (3 y)}$

Step 4

Simplify $3 x^{0} y^{2} \cdot (3 y)$ .

$\frac{3 x^{- 7} y^{- 2}}{3 y^{2} \cdot (3 y)}$

Step 5

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 5.1

Move $y$ .

$\frac{3 x^{- 7} y^{- 2}}{3 (y \cdot y^{2}) \cdot 3}$

Step 5.2

Multiply $y$ by $y^{2}$ .

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Step 5.2.1

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

$\frac{3 x^{- 7} y^{- 2}}{3 (y^{1} y^{2}) \cdot 3}$

Step 5.2.2

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

$\frac{3 x^{- 7} y^{- 2}}{3 y^{1 + 2} \cdot 3}$

Step 5.3

Add $1$ and $2$ .

$\frac{3 x^{- 7} y^{- 2}}{3 y^{3} \cdot 3}$

Step 6

Move $x^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 y^{- 2}}{3 y^{3} \cdot 3 x^{7}}$

Step 7

Move $y^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3}{3 y^{3} \cdot 3 x^{7} y^{2}}$

Step 8

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

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Step 8.1

Move $y^{2}$ .

$\frac{3}{3 (y^{2} y^{3}) \cdot 3 x^{7}}$

Step 8.2

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

$\frac{3}{3 y^{2 + 3} \cdot 3 x^{7}}$

Step 8.3

Add $2$ and $3$ .

$\frac{3}{3 y^{5} \cdot 3 x^{7}}$

Step 9

Cancel the common factor of $3$ .

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Step 9.1

Cancel the common factor.

$\frac{3}{3 y^{5} \cdot 3 x^{7}}$

Step 9.2

Rewrite the expression.

$\frac{1}{y^{5} \cdot 3 x^{7}}$

Step 10

Move $3$ to the left of $y^{5}$ .

$\frac{1}{3 y^{5} x^{7}}$