Algebra Examples

$(x^{3} y^{- 5}) (2 x^{- 4} y^{2}) (4 x y^{5})$

Step 1

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

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Step 1.1

Move $x^{- 4}$ .

$x^{- 4} x^{3} y^{- 5} (2 y^{2}) (4 x y^{5})$

Step 1.2

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

$x^{- 4 + 3} y^{- 5} (2 y^{2}) (4 x y^{5})$

Step 1.3

Add $- 4$ and $3$ .

$x^{- 1} y^{- 5} (2 y^{2}) (4 x y^{5})$

Step 2

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

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Step 2.1

Move $x$ .

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

Step 2.2

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

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Step 2.2.1

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

$x^{1} x^{- 1} y^{- 5} (2 y^{2}) (4 y^{5})$

Step 2.2.2

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

$x^{1 - 1} y^{- 5} (2 y^{2}) (4 y^{5})$

Step 2.3

Subtract $1$ from $1$ .

$x^{0} y^{- 5} (2 y^{2}) (4 y^{5})$

Step 3

Simplify $x^{0} y^{- 5} (2 y^{2}) (4 y^{5})$ .

$y^{- 5} (2 y^{2}) (4 y^{5})$

Step 4

Multiply $y^{- 5}$ by $y^{2}$ by adding the exponents.

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Step 4.1

Move $y^{2}$ .

$y^{2} y^{- 5} \cdot 2 (4 y^{5})$

Step 4.2

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

$y^{2 - 5} \cdot 2 (4 y^{5})$

Step 4.3

Subtract $5$ from $2$ .

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

Step 5

Multiply $y^{- 3}$ by $y^{5}$ by adding the exponents.

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Step 5.1

Move $y^{5}$ .

$y^{5} y^{- 3} \cdot 2 \cdot 4$

Step 5.2

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

$y^{5 - 3} \cdot 2 \cdot 4$

Step 5.3

Subtract $3$ from $5$ .

$y^{2} \cdot 2 \cdot 4$

Step 6

Move $2$ to the left of $y^{2}$ .

$2 \cdot y^{2} \cdot 4$

Step 7

Multiply $4$ by $2$ .

$8 y^{2}$