Algebra Examples

$- \frac{4 u^{8}}{3 {(u^{- 1})}^{4}}$

Step 1

Simplify the denominator.

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Step 1.1

Multiply the exponents in ${(u^{- 1})}^{4}$ .

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Step 1.1.1

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

$- \frac{4 u^{8}}{3 u^{- 1 \cdot 4}}$

Step 1.1.2

Multiply $- 1$ by $4$ .

$- \frac{4 u^{8}}{3 u^{- 4}}$

Step 1.2

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

$- \frac{4 u^{8}}{3 \frac{1}{u^{4}}}$

Step 2

Combine $3$ and $\frac{1}{u^{4}}$ .

$- \frac{4 u^{8}}{\frac{3}{u^{4}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- (4 u^{8} \frac{u^{4}}{3})$

Step 4

Multiply $4 u^{8} \frac{u^{4}}{3}$ .

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Step 4.1

Combine $4$ and $\frac{u^{4}}{3}$ .

$- (u^{8} \frac{4 u^{4}}{3})$

Step 4.2

Combine $u^{8}$ and $\frac{4 u^{4}}{3}$ .

$- \frac{u^{8} (4 u^{4})}{3}$

Step 4.3

Multiply $u^{8}$ by $u^{4}$ by adding the exponents.

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Step 4.3.1

Move $u^{4}$ .

$- \frac{u^{4} u^{8} \cdot 4}{3}$

Step 4.3.2

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

$- \frac{u^{4 + 8} \cdot 4}{3}$

Step 4.3.3

Add $4$ and $8$ .

$- \frac{u^{12} \cdot 4}{3}$

Step 5

Move $4$ to the left of $u^{12}$ .

$- \frac{4 u^{12}}{3}$