Algebra Examples

$\frac{x^{- 6} y^{- 4} z^{- 5}}{x^{4} y^{- 3} z^{8}}$

Step 1

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

$\frac{y^{- 4} z^{- 5}}{x^{4} y^{- 3} z^{8} x^{6}}$

Step 2

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

$\frac{z^{- 5}}{x^{4} y^{- 3} z^{8} x^{6} y^{4}}$

Step 3

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

$\frac{1}{x^{4} y^{- 3} z^{8} x^{6} y^{4} z^{5}}$

Step 4

Simplify the denominator.

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Step 4.1

Multiply $x^{4}$ by $x^{6}$ by adding the exponents.

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Step 4.1.1

Move $x^{6}$ .

$\frac{1}{x^{6} x^{4} y^{- 3} z^{8} y^{4} z^{5}}$

Step 4.1.2

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

$\frac{1}{x^{6 + 4} y^{- 3} z^{8} y^{4} z^{5}}$

Step 4.1.3

Add $6$ and $4$ .

$\frac{1}{x^{10} y^{- 3} z^{8} y^{4} z^{5}}$

Step 4.2

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

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Step 4.2.1

Move $y^{4}$ .

$\frac{1}{x^{10} (y^{4} y^{- 3}) z^{8} z^{5}}$

Step 4.2.2

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

$\frac{1}{x^{10} y^{4 - 3} z^{8} z^{5}}$

Step 4.2.3

Subtract $3$ from $4$ .

$\frac{1}{x^{10} y^{1} z^{8} z^{5}}$

Step 4.3

Simplify $x^{10} y^{1} z^{8}$ .

$\frac{1}{x^{10} y z^{8} z^{5}}$

Step 4.4

Multiply $z^{8}$ by $z^{5}$ by adding the exponents.

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Step 4.4.1

Move $z^{5}$ .

$\frac{1}{x^{10} y (z^{5} z^{8})}$

Step 4.4.2

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

$\frac{1}{x^{10} y z^{5 + 8}}$

Step 4.4.3

Add $5$ and $8$ .

$\frac{1}{x^{10} y z^{13}}$