Calculus Examples

$\frac{u^{4} u^{- 7}}{\frac{x^{8}}{u^{2}}}$

Step 1

Multiply $u^{4}$ by $u^{- 7}$ by adding the exponents.

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Step 1.1

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

$\frac{u^{4 - 7}}{\frac{x^{8}}{u^{2}}}$

Step 1.2

Subtract $7$ from $4$ .

$\frac{u^{- 3}}{\frac{x^{8}}{u^{2}}}$

Step 2

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

$\frac{1}{\frac{x^{8}}{u^{2}} u^{3}}$

Step 3

Combine $\frac{x^{8}}{u^{2}}$ and $u^{3}$ .

$\frac{1}{\frac{x^{8} u^{3}}{u^{2}}}$

Step 4

Cancel the common factor of $u^{3}$ and $u^{2}$ .

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Step 4.1

Factor $u^{2}$ out of $x^{8} u^{3}$ .

$\frac{1}{\frac{u^{2} (x^{8} u)}{u^{2}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{1}{\frac{u^{2} (x^{8} u)}{u^{2} \cdot 1}}$

Step 4.2.2

Cancel the common factor.

$\frac{1}{\frac{u^{2} (x^{8} u)}{u^{2} \cdot 1}}$

Step 4.2.3

Rewrite the expression.

$\frac{1}{\frac{x^{8} u}{1}}$

Step 4.2.4

Divide $x^{8} u$ by $1$ .

$\frac{1}{x^{8} u}$