Pre-Algebra Examples

$\frac{12 x^{- 3} y^{- 2} z^{- 8}}{30 x^{- 6} y^{- 4} z^{- 1}}$

Step 1

Move $z^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{12 x^{- 3} y^{- 2}}{30 x^{- 6} y^{- 4} z^{- 1} z^{8}}$

Step 2

Multiply $z^{- 1}$ by $z^{8}$ by adding the exponents.

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Step 2.1

Move $z^{8}$ .

$\frac{12 x^{- 3} y^{- 2}}{30 x^{- 6} y^{- 4} (z^{8} z^{- 1})}$

Step 2.2

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

$\frac{12 x^{- 3} y^{- 2}}{30 x^{- 6} y^{- 4} z^{8 - 1}}$

Step 2.3

Subtract $1$ from $8$ .

$\frac{12 x^{- 3} y^{- 2}}{30 x^{- 6} y^{- 4} z^{7}}$

Step 3

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

$\frac{12 x^{- 3} y^{- 2} x^{6}}{30 y^{- 4} z^{7}}$

Step 4

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

$\frac{12 x^{- 3} y^{- 2} x^{6} y^{4}}{30 z^{7}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $x^{- 3}$ by $x^{6}$ by adding the exponents.

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Step 5.1.1

Move $x^{6}$ .

$\frac{12 (x^{6} x^{- 3}) y^{- 2} y^{4}}{30 z^{7}}$

Step 5.1.2

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

$\frac{12 x^{6 - 3} y^{- 2} y^{4}}{30 z^{7}}$

Step 5.1.3

Subtract $3$ from $6$ .

$\frac{12 x^{3} y^{- 2} y^{4}}{30 z^{7}}$

Step 5.2

Multiply $y^{- 2}$ by $y^{4}$ by adding the exponents.

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Step 5.2.1

Move $y^{4}$ .

$\frac{12 x^{3} (y^{4} y^{- 2})}{30 z^{7}}$

Step 5.2.2

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

$\frac{12 x^{3} y^{4 - 2}}{30 z^{7}}$

Step 5.2.3

Subtract $2$ from $4$ .

$\frac{12 x^{3} y^{2}}{30 z^{7}}$

Step 6

Cancel the common factor of $12$ and $30$ .

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Step 6.1

Factor $6$ out of $12 x^{3} y^{2}$ .

$\frac{6 (2 x^{3} y^{2})}{30 z^{7}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $6$ out of $30 z^{7}$ .

$\frac{6 (2 x^{3} y^{2})}{6 (5 z^{7})}$

Step 6.2.2

Cancel the common factor.

$\frac{6 (2 x^{3} y^{2})}{6 (5 z^{7})}$

Step 6.2.3

Rewrite the expression.

$\frac{2 x^{3} y^{2}}{5 z^{7}}$