Pre-Algebra Examples

$\frac{\frac{u^{- 4} v^{2}}{w^{2} s^{- 4}}}{\frac{u^{- 2} v^{6}}{w^{4} s^{- 2}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{u^{- 4} v^{2}}{w^{2} s^{- 4}} \cdot \frac{w^{4} s^{- 2}}{u^{- 2} v^{6}}$

Step 2

Combine.

$\frac{u^{- 4} v^{2} (w^{4} s^{- 2})}{w^{2} s^{- 4} (u^{- 2} v^{6})}$

Step 3

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

$\frac{v^{2} (w^{4} s^{- 2})}{w^{2} s^{- 4} (u^{- 2} v^{6}) u^{4}}$

Step 4

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

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Step 4.1

Move $u^{4}$ .

$\frac{v^{2} (w^{4} s^{- 2})}{w^{2} s^{- 4} (u^{4} u^{- 2} v^{6})}$

Step 4.2

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

$\frac{v^{2} (w^{4} s^{- 2})}{w^{2} s^{- 4} (u^{4 - 2} v^{6})}$

Step 4.3

Subtract $2$ from $4$ .

$\frac{v^{2} (w^{4} s^{- 2})}{w^{2} s^{- 4} (u^{2} v^{6})}$

Step 5

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

$\frac{v^{2} (w^{4} s^{- 2}) s^{4}}{w^{2} (u^{2} v^{6})}$

Step 6

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

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Step 6.1

Move $s^{4}$ .

$\frac{v^{2} (w^{4} (s^{4} s^{- 2}))}{w^{2} (u^{2} v^{6})}$

Step 6.2

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

$\frac{v^{2} (w^{4} s^{4 - 2})}{w^{2} (u^{2} v^{6})}$

Step 6.3

Subtract $2$ from $4$ .

$\frac{v^{2} (w^{4} s^{2})}{w^{2} (u^{2} v^{6})}$

Step 7

Cancel the common factors.

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Step 7.1

Factor $v^{2}$ out of $w^{2} (u^{2} v^{6})$ .

$\frac{v^{2} (w^{4} s^{2})}{v^{2} (w^{2} (u^{2} v^{4}))}$

Step 7.2

Cancel the common factor.

$\frac{v^{2} (w^{4} s^{2})}{v^{2} (w^{2} (u^{2} v^{4}))}$

Step 7.3

Rewrite the expression.

$\frac{w^{4} s^{2}}{w^{2} (u^{2} v^{4})}$

Step 8

Cancel the common factor of $w^{4}$ and $w^{2}$ .

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Step 8.1

Factor $w^{2}$ out of $w^{4} s^{2}$ .

$\frac{w^{2} (w^{2} s^{2})}{w^{2} (u^{2} v^{4})}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Cancel the common factor.

$\frac{w^{2} (w^{2} s^{2})}{w^{2} (u^{2} v^{4})}$

Step 8.2.2

Rewrite the expression.

$\frac{w^{2} s^{2}}{u^{2} v^{4}}$