Basic Math Examples

$\frac{- 3 x^{- 4} y^{2} z^{6}}{- 15 x^{- 3} y^{7} z^{- 2}}$

Step 1

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

$\frac{- 3 y^{2} z^{6}}{- 15 x^{- 3} y^{7} z^{- 2} x^{4}}$

Step 2

Simplify the denominator.

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Step 2.1

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

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Step 2.1.1

Move $x^{4}$ .

$\frac{- 3 y^{2} z^{6}}{- 15 (x^{4} x^{- 3}) y^{7} z^{- 2}}$

Step 2.1.2

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

$\frac{- 3 y^{2} z^{6}}{- 15 x^{4 - 3} y^{7} z^{- 2}}$

Step 2.1.3

Subtract $3$ from $4$ .

$\frac{- 3 y^{2} z^{6}}{- 15 x^{1} y^{7} z^{- 2}}$

Step 2.2

Simplify $- 15 x^{1} y^{7} z^{- 2}$ .

$\frac{- 3 y^{2} z^{6}}{- 15 x y^{7} z^{- 2}}$

Step 3

Move $z^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 3 y^{2} z^{6} z^{2}}{- 15 x y^{7}}$

Step 4

Multiply $z^{6}$ by $z^{2}$ by adding the exponents.

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Step 4.1

Move $z^{2}$ .

$\frac{- 3 y^{2} (z^{2} z^{6})}{- 15 x y^{7}}$

Step 4.2

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

$\frac{- 3 y^{2} z^{2 + 6}}{- 15 x y^{7}}$

Step 4.3

Add $2$ and $6$ .

$\frac{- 3 y^{2} z^{8}}{- 15 x y^{7}}$

Step 5

Cancel the common factor of $- 3$ and $- 15$ .

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Step 5.1

Factor $- 3$ out of $- 3 y^{2} z^{8}$ .

$\frac{- 3 (y^{2} z^{8})}{- 15 x y^{7}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $- 3$ out of $- 15 x y^{7}$ .

$\frac{- 3 (y^{2} z^{8})}{- 3 (5 x y^{7})}$

Step 5.2.2

Cancel the common factor.

$\frac{- 3 (y^{2} z^{8})}{- 3 (5 x y^{7})}$

Step 5.2.3

Rewrite the expression.

$\frac{y^{2} z^{8}}{5 x y^{7}}$

Step 6

Cancel the common factor of $y^{2}$ and $y^{7}$ .

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Step 6.1

Factor $y^{2}$ out of $y^{2} z^{8}$ .

$\frac{y^{2} (z^{8})}{5 x y^{7}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y^{2}$ out of $5 x y^{7}$ .

$\frac{y^{2} (z^{8})}{y^{2} (5 x y^{5})}$

Step 6.2.2

Cancel the common factor.

$\frac{y^{2} z^{8}}{y^{2} (5 x y^{5})}$

Step 6.2.3

Rewrite the expression.

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