Write the Fraction in Simplest Form (-4u^8)/(3(u^-1)^4)

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

Simplify the denominator.

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

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

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

Multiply $- 1$ by $4$ .

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

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

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

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

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

Multiply the numerator by the reciprocal of the denominator.

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

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

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

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

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

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

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

Move $u^{4}$ .

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

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

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

Add $4$ and $8$ .

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

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

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

Move the negative in front of the fraction.

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