Algebra Examples

$\frac{10 x^{6} y^{12}}{- 5 x^{- 2} y^{- 6}}$

Step 1

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

$\frac{10 x^{6} y^{12} x^{2}}{- 5 y^{- 6}}$

Step 2

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

$\frac{10 x^{6} y^{12} x^{2} y^{6}}{- 5}$

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

Move $x^{2}$ .

$\frac{10 (x^{2} x^{6}) y^{12} y^{6}}{- 5}$

Step 3.1.2

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

$\frac{10 x^{2 + 6} y^{12} y^{6}}{- 5}$

Step 3.1.3

Add $2$ and $6$ .

$\frac{10 x^{8} y^{12} y^{6}}{- 5}$

Step 3.2

Multiply $y^{12}$ by $y^{6}$ by adding the exponents.

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Step 3.2.1

Move $y^{6}$ .

$\frac{10 x^{8} (y^{6} y^{12})}{- 5}$

Step 3.2.2

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

$\frac{10 x^{8} y^{6 + 12}}{- 5}$

Step 3.2.3

Add $6$ and $12$ .

$\frac{10 x^{8} y^{18}}{- 5}$

Step 4

Cancel the common factor of $10$ and $- 5$ .

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Step 4.1

Factor $5$ out of $10 x^{8} y^{18}$ .

$\frac{5 (2 x^{8} y^{18})}{- 5}$

Step 4.2

Move the negative one from the denominator of $\frac{2 x^{8} y^{18}}{- 1}$ .

$- 1 \cdot (2 x^{8} y^{18})$

Step 5

Simplify the expression.

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Step 5.1

Rewrite $- 1 \cdot (2 x^{8} y^{18})$ as $- (2 x^{8} y^{18})$ .

$- (2 x^{8} y^{18})$

Step 5.2

Multiply $2$ by $- 1$ .

$- 2 x^{8} y^{18}$