Algebra Examples

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

Step 1

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

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Step 1.1

Move $x^{- 3}$ .

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

Step 1.2

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

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

Step 1.3

Add $- 3$ and $4$ .

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

Step 2

Simplify $2 x^{1} y^{2} \cdot y$ .

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

Step 3

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

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Step 3.1

Move $y$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $1$ and $2$ .

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

Step 4

Move ${(2 x^{2} y^{2} \cdot (y x^{- 1}))}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 5

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

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Step 5.1

Move $x^{- 1}$ .

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

Step 5.2

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

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

Step 5.3

Add $- 1$ and $2$ .

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

Step 6

Simplify $2 x^{1} y^{2} \cdot y$ .

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

Step 7

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

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Step 7.1

Move $y$ .

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

Step 7.2

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

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Step 7.2.1

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

$2 x y^{3} {(2 x (y^{1} y^{2}))}^{3}$

Step 7.2.2

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

$2 x y^{3} {(2 x y^{1 + 2})}^{3}$

Step 7.3

Add $1$ and $2$ .

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

Step 8

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 8.1

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

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

Step 8.2

Apply the product rule to $2 x$ .

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

Step 9

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

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Step 9.1

Move $2^{3}$ .

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

Step 9.2

Multiply $2^{3}$ by $2$ .

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Step 9.2.1

Raise $2$ to the power of $1$ .

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

Step 9.2.2

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

$2^{3 + 1} x y^{3} (x^{3} {(y^{3})}^{3})$

Step 9.3

Add $3$ and $1$ .

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

Step 10

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

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Step 10.1

Move $x^{3}$ .

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

Step 10.2

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

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Step 10.2.1

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

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

Step 10.2.2

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

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

Step 10.3

Add $3$ and $1$ .

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

Step 11

Raise $2$ to the power of $4$ .

$16 x^{4} y^{3} {(y^{3})}^{3}$

Step 12

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

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Step 12.1

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

$16 x^{4} y^{3} y^{3 \cdot 3}$

Step 12.2

Multiply $3$ by $3$ .

$16 x^{4} y^{3} y^{9}$

Step 13

Multiply $y^{3}$ by $y^{9}$ by adding the exponents.

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Step 13.1

Move $y^{9}$ .

$16 x^{4} (y^{9} y^{3})$

Step 13.2

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

$16 x^{4} y^{9 + 3}$

Step 13.3

Add $9$ and $3$ .

$16 x^{4} y^{12}$