Algebra Examples

$\frac{4 {(v^{- 1} s^{- 1})}^{- 1}}{2 v^{10} s^{- 1}}$

Step 1

Move ${(v^{- 1} s^{- 1})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{2 v^{10} s^{- 1} (v^{- 1} s^{- 1})}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $v^{10}$ by $v^{- 1}$ by adding the exponents.

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Step 2.1.1

Move $v^{- 1}$ .

$\frac{4}{2 (v^{- 1} v^{10}) s^{- 1} s^{- 1}}$

Step 2.1.2

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

$\frac{4}{2 v^{- 1 + 10} s^{- 1} s^{- 1}}$

Step 2.1.3

Add $- 1$ and $10$ .

$\frac{4}{2 v^{9} s^{- 1} s^{- 1}}$

Step 2.2

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

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Step 2.2.1

Move $s^{- 1}$ .

$\frac{4}{2 v^{9} (s^{- 1} s^{- 1})}$

Step 2.2.2

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

$\frac{4}{2 v^{9} s^{- 1 - 1}}$

Step 2.2.3

Subtract $1$ from $- 1$ .

$\frac{4}{2 v^{9} s^{- 2}}$

Step 3

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

$\frac{4 s^{2}}{2 v^{9}}$

Step 4

Cancel the common factor of $4$ and $2$ .

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Step 4.1

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

$\frac{2 (2 s^{2})}{2 v^{9}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2 v^{9}$ .

$\frac{2 (2 s^{2})}{2 (v^{9})}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (2 s^{2})}{2 v^{9}}$

Step 4.2.3

Rewrite the expression.

$\frac{2 s^{2}}{v^{9}}$