Algebra Examples

$\frac{x^{8} x^{3} y^{- 2}}{x^{- 1} y^{- 5}}$

Step 1

Multiply $x^{8}$ by $x^{3}$ by adding the exponents.

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Step 1.1

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

$\frac{x^{8 + 3} y^{- 2}}{x^{- 1} y^{- 5}}$

Step 1.2

Add $8$ and $3$ .

$\frac{x^{11} y^{- 2}}{x^{- 1} y^{- 5}}$

Step 2

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

$\frac{x^{11} y^{- 2} x}{y^{- 5}}$

Step 3

Move $y^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$x^{11} y^{- 2} x y^{5}$

Step 4

Multiply $x^{11}$ by $x$ by adding the exponents.

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Step 4.1

Move $x$ .

$x \cdot x^{11} y^{- 2} y^{5}$

Step 4.2

Multiply $x$ by $x^{11}$ .

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Step 4.2.1

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

$x^{1} x^{11} y^{- 2} y^{5}$

Step 4.2.2

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

$x^{1 + 11} y^{- 2} y^{5}$

Step 4.3

Add $1$ and $11$ .

$x^{12} y^{- 2} y^{5}$

Step 5

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

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Step 5.1

Move $y^{5}$ .

$x^{12} (y^{5} y^{- 2})$

Step 5.2

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

$x^{12} y^{5 - 2}$

Step 5.3

Subtract $2$ from $5$ .

$x^{12} y^{3}$