Basic Math Examples

$\frac{18 u^{4} v^{- 5}}{u^{- 1} v^{7}}$

Step 1

Move $v^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{18 u^{4}}{u^{- 1} v^{7} v^{5}}$

Step 2

Multiply $v^{7}$ by $v^{5}$ by adding the exponents.

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Step 2.1

Move $v^{5}$ .

$\frac{18 u^{4}}{u^{- 1} (v^{5} v^{7})}$

Step 2.2

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

$\frac{18 u^{4}}{u^{- 1} v^{5 + 7}}$

Step 2.3

Add $5$ and $7$ .

$\frac{18 u^{4}}{u^{- 1} v^{12}}$

Step 3

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

$\frac{18 u^{4} u}{v^{12}}$

Step 4

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

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Step 4.1

Move $u$ .

$\frac{18 (u \cdot u^{4})}{v^{12}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{18 (u^{1} u^{4})}{v^{12}}$

Step 4.2.2

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

$\frac{18 u^{1 + 4}}{v^{12}}$

Step 4.3

Add $1$ and $4$ .

$\frac{18 u^{5}}{v^{12}}$