Algebra Examples

$\frac{x y^{- 6} z^{- 3}}{x^{- 4} y^{- 5} z}$

Step 1

Move $y^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x z^{- 3}}{x^{- 4} y^{- 5} z y^{6}}$

Step 2

Move $z^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x}{x^{- 4} y^{- 5} z y^{6} z^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $y^{- 5}$ by $y^{6}$ by adding the exponents.

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Step 3.1.1

Move $y^{6}$ .

$\frac{x}{x^{- 4} (y^{6} y^{- 5}) z \cdot z^{3}}$

Step 3.1.2

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

$\frac{x}{x^{- 4} y^{6 - 5} z \cdot z^{3}}$

Step 3.1.3

Subtract $5$ from $6$ .

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

Step 3.2

Simplify $x^{- 4} y^{1} z$ .

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

Step 3.3

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

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Step 3.3.1

Move $z^{3}$ .

$\frac{x}{x^{- 4} y (z^{3} z)}$

Step 3.3.2

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

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Step 3.3.2.1

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

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

Step 3.3.2.2

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

$\frac{x}{x^{- 4} y z^{3 + 1}}$

Step 3.3.3

Add $3$ and $1$ .

$\frac{x}{x^{- 4} y z^{4}}$

Step 4

Move $x^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x \cdot x^{4}}{y z^{4}}$

Step 5

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

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Step 5.1

Multiply $x$ by $x^{4}$ .

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Step 5.1.1

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

$\frac{x^{1} x^{4}}{y z^{4}}$

Step 5.1.2

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

$\frac{x^{1 + 4}}{y z^{4}}$

Step 5.2

Add $1$ and $4$ .

$\frac{x^{5}}{y z^{4}}$