Basic Math Examples

$\frac{2 u^{- 4} v^{4} \cdot (2 u v^{- 4})}{{(u v^{- 3})}^{2}}$

Step 1

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

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Step 1.1

Move $u$ .

$\frac{2 (u \cdot u^{- 4}) v^{4} \cdot (2 v^{- 4})}{{(u v^{- 3})}^{2}}$

Step 1.2

Multiply $u$ by $u^{- 4}$ .

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Step 1.2.1

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

$\frac{2 (u^{1} u^{- 4}) v^{4} \cdot (2 v^{- 4})}{{(u v^{- 3})}^{2}}$

Step 1.2.2

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

$\frac{2 u^{1 - 4} v^{4} \cdot (2 v^{- 4})}{{(u v^{- 3})}^{2}}$

Step 1.3

Subtract $4$ from $1$ .

$\frac{2 u^{- 3} v^{4} \cdot (2 v^{- 4})}{{(u v^{- 3})}^{2}}$

Step 2

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

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Step 2.1

Move $v^{- 4}$ .

$\frac{2 u^{- 3} (v^{- 4} v^{4}) \cdot 2}{{(u v^{- 3})}^{2}}$

Step 2.2

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

$\frac{2 u^{- 3} v^{- 4 + 4} \cdot 2}{{(u v^{- 3})}^{2}}$

Step 2.3

Add $- 4$ and $4$ .

$\frac{2 u^{- 3} v^{0} \cdot 2}{{(u v^{- 3})}^{2}}$

Step 3

Multiply.

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Step 3.1

Simplify $2 u^{- 3} v^{0} \cdot 2$ .

$\frac{2 u^{- 3} \cdot 2}{{(u v^{- 3})}^{2}}$

Step 3.2

Move $u^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 \cdot 2}{{(u v^{- 3})}^{2} u^{3}}$

Step 3.3

Multiply $2$ by $2$ .

$\frac{4}{{(u v^{- 3})}^{2} u^{3}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $u v^{- 3}$ .

$\frac{4}{u^{2} {(v^{- 3})}^{2} u^{3}}$

Step 4.2

Multiply $u^{2}$ by $u^{3}$ by adding the exponents.

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Step 4.2.1

Move $u^{3}$ .

$\frac{4}{u^{3} u^{2} {(v^{- 3})}^{2}}$

Step 4.2.2

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

$\frac{4}{u^{3 + 2} {(v^{- 3})}^{2}}$

Step 4.2.3

Add $3$ and $2$ .

$\frac{4}{u^{5} {(v^{- 3})}^{2}}$

Step 4.3

Multiply the exponents in ${(v^{- 3})}^{2}$ .

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Step 4.3.1

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

$\frac{4}{u^{5} v^{- 3 \cdot 2}}$

Step 4.3.2

Multiply $- 3$ by $2$ .

$\frac{4}{u^{5} v^{- 6}}$

Step 4.4

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

$\frac{4}{u^{5} \frac{1}{v^{6}}}$

Step 5

Combine $u^{5}$ and $\frac{1}{v^{6}}$ .

$\frac{4}{\frac{u^{5}}{v^{6}}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$4 \frac{v^{6}}{u^{5}}$

Step 7

Combine $4$ and $\frac{v^{6}}{u^{5}}$ .

$\frac{4 v^{6}}{u^{5}}$