Basic Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $2 u^{4} v^{- 4}$ .

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

Step 1.2

Apply the product rule to $2 u^{4}$ .

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

Step 1.3

Raise $2$ to the power of $2$ .

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

Step 1.4

Multiply the exponents in ${(u^{4})}^{2}$ .

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Step 1.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{u v}{4 u^{4 \cdot 2} {(v^{- 4})}^{2}}$

Step 1.4.2

Multiply $4$ by $2$ .

$\frac{u v}{4 u^{8} {(v^{- 4})}^{2}}$

Step 1.5

Multiply the exponents in ${(v^{- 4})}^{2}$ .

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Step 1.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{u v}{4 u^{8} v^{- 4 \cdot 2}}$

Step 1.5.2

Multiply $- 4$ by $2$ .

$\frac{u v}{4 u^{8} v^{- 8}}$

Step 1.6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{u v}{4 u^{8} \frac{1}{v^{8}}}$

Step 1.7

Combine exponents.

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Step 1.7.1

Combine $4$ and $\frac{1}{v^{8}}$ .

$\frac{u v}{u^{8} \frac{4}{v^{8}}}$

Step 1.7.2

Combine $u^{8}$ and $\frac{4}{v^{8}}$ .

$\frac{u v}{\frac{u^{8} \cdot 4}{v^{8}}}$

Step 1.8

Move $4$ to the left of $u^{8}$ .

$\frac{u v}{\frac{4 u^{8}}{v^{8}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$u v \frac{v^{8}}{4 u^{8}}$

Step 3

Cancel the common factor of $u$ .

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Step 3.1

Factor $u$ out of $u v$ .

$u (v) \frac{v^{8}}{4 u^{8}}$

Step 3.2

Factor $u$ out of $4 u^{8}$ .

$u (v) \frac{v^{8}}{u (4 u^{7})}$

Step 3.3

Cancel the common factor.

$u v \frac{v^{8}}{u (4 u^{7})}$

Step 3.4

Rewrite the expression.

$v \frac{v^{8}}{4 u^{7}}$

Step 4

Combine $v$ and $\frac{v^{8}}{4 u^{7}}$ .

$\frac{v \cdot v^{8}}{4 u^{7}}$

Step 5

Multiply $v$ by $v^{8}$ by adding the exponents.

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Step 5.1

Multiply $v$ by $v^{8}$ .

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Step 5.1.1

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

$\frac{v^{1} v^{8}}{4 u^{7}}$

Step 5.1.2

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

$\frac{v^{1 + 8}}{4 u^{7}}$

Step 5.2

Add $1$ and $8$ .

$\frac{v^{9}}{4 u^{7}}$