Algebra Examples

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

Step 1

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

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Step 1.1

Move $x^{4}$ .

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

Step 1.2

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

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

Step 1.3

Add $4$ and $2$ .

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

Step 2

Multiply $x^{6}$ by $x^{3}$ by adding the exponents.

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Step 2.1

Move $x^{3}$ .

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

Step 2.2

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

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

Step 2.3

Add $3$ and $6$ .

$x^{9} y^{2} \cdot (4 y^{- 1}) \cdot y^{- 4}$

Step 3

Multiply $y^{2}$ by $y^{- 1}$ by adding the exponents.

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Step 3.1

Move $y^{- 1}$ .

$x^{9} (y^{- 1} y^{2}) \cdot 4 \cdot y^{- 4}$

Step 3.2

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

$x^{9} y^{- 1 + 2} \cdot 4 \cdot y^{- 4}$

Step 3.3

Add $- 1$ and $2$ .

$x^{9} y^{1} \cdot 4 \cdot y^{- 4}$

Step 4

Simplify $x^{9} y^{1} \cdot 4 \cdot y^{- 4}$ .

$x^{9} y \cdot 4 \cdot y^{- 4}$

Step 5

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

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Step 5.1

Move $y^{- 4}$ .

$x^{9} (y^{- 4} y) \cdot 4$

Step 5.2

Multiply $y^{- 4}$ by $y$ .

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Step 5.2.1

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

$x^{9} (y^{- 4} y^{1}) \cdot 4$

Step 5.2.2

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

$x^{9} y^{- 4 + 1} \cdot 4$

Step 5.3

Add $- 4$ and $1$ .

$x^{9} y^{- 3} \cdot 4$

Step 6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x^{9} \frac{1}{y^{3}} \cdot 4$

Step 7

Combine $x^{9}$ and $\frac{1}{y^{3}}$ .

$\frac{x^{9}}{y^{3}} \cdot 4$

Step 8

Combine $\frac{x^{9}}{y^{3}}$ and $4$ .

$\frac{x^{9} \cdot 4}{y^{3}}$

Step 9

Move $4$ to the left of $x^{9}$ .

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