Algebra Examples

$\frac{x^{- 8} y^{7} \cdot 2 x^{4} y^{8}}{6 x^{- 3} y^{7} \cdot x^{4}}$

Step 1

Multiply $x^{- 8}$ by $x^{4}$ by adding the exponents.

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Step 1.1

Move $x^{4}$ .

$\frac{x^{4} x^{- 8} y^{7} \cdot (2 y^{8})}{6 x^{- 3} y^{7} \cdot x^{4}}$

Step 1.2

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

$\frac{x^{4 - 8} y^{7} \cdot (2 y^{8})}{6 x^{- 3} y^{7} \cdot x^{4}}$

Step 1.3

Subtract $8$ from $4$ .

$\frac{x^{- 4} y^{7} \cdot (2 y^{8})}{6 x^{- 3} y^{7} \cdot x^{4}}$

Step 2

Multiply $y^{7}$ by $y^{8}$ by adding the exponents.

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Step 2.1

Move $y^{8}$ .

$\frac{x^{- 4} (y^{8} y^{7}) \cdot 2}{6 x^{- 3} y^{7} \cdot x^{4}}$

Step 2.2

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

$\frac{x^{- 4} y^{8 + 7} \cdot 2}{6 x^{- 3} y^{7} \cdot x^{4}}$

Step 2.3

Add $8$ and $7$ .

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

Step 3

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

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Step 3.1

Move $x^{4}$ .

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

Step 3.2

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

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

Step 3.3

Subtract $3$ from $4$ .

$\frac{x^{- 4} y^{15} \cdot 2}{6 x^{1} y^{7}}$

Step 4

Simplify $6 x^{1} y^{7}$ .

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

Step 5

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

$\frac{y^{15} \cdot 2}{6 x y^{7} x^{4}}$

Step 6

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

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Step 6.1

Move $x^{4}$ .

$\frac{y^{15} \cdot 2}{6 (x^{4} x) y^{7}}$

Step 6.2

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

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Step 6.2.1

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

$\frac{y^{15} \cdot 2}{6 (x^{4} x^{1}) y^{7}}$

Step 6.2.2

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

$\frac{y^{15} \cdot 2}{6 x^{4 + 1} y^{7}}$

Step 6.3

Add $4$ and $1$ .

$\frac{y^{15} \cdot 2}{6 x^{5} y^{7}}$

Step 7

Cancel the common factor of $y^{15}$ and $y^{7}$ .

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Step 7.1

Factor $y^{7}$ out of $y^{15} \cdot 2$ .

$\frac{y^{7} (y^{8} \cdot 2)}{6 x^{5} y^{7}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $y^{7}$ out of $6 x^{5} y^{7}$ .

$\frac{y^{7} (y^{8} \cdot 2)}{y^{7} (6 x^{5})}$

Step 7.2.2

Cancel the common factor.

$\frac{y^{7} (y^{8} \cdot 2)}{y^{7} (6 x^{5})}$

Step 7.2.3

Rewrite the expression.

$\frac{y^{8} \cdot 2}{6 x^{5}}$

Step 8

Cancel the common factor of $2$ and $6$ .

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Step 8.1

Factor $2$ out of $y^{8} \cdot 2$ .

$\frac{2 \cdot y^{8}}{6 x^{5}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $6 x^{5}$ .

$\frac{2 \cdot y^{8}}{2 (3 x^{5})}$

Step 8.2.2

Cancel the common factor.

$\frac{2 \cdot y^{8}}{2 (3 x^{5})}$

Step 8.2.3

Rewrite the expression.

$\frac{y^{8}}{3 x^{5}}$