# How do you multiply t^ { - 1} u ^ { - 1} \cdot t u ^ { - 5} \cdot t ^ { - 4} u ^ { 0}?

##### 2 Answers
Jul 25, 2017

$= \frac{1}{{t}^{4} {u}^{6}}$

#### Explanation:

Recall two of the laws of indices.

${x}^{-} m = \frac{1}{x} ^ m \text{ and } \frac{1}{x} ^ - n = {x}^{n}$

x^0 = 1" "(0^0 is undefined)

$\textcolor{red}{{t}^{-} 1 {u}^{-} 1} \times t \textcolor{b l u e}{{u}^{-} 5} \times \textcolor{g r e e n}{{t}^{-} 4} \textcolor{m a \ge n t a}{{u}^{0}}$

$= \frac{1}{\textcolor{red}{t u}} \times \frac{t}{\textcolor{b l u e}{{u}^{5}}} \times \frac{1}{\textcolor{g r e e n}{{t}^{4}}} \times \textcolor{m a \ge n t a}{1} \text{ } \leftarrow$ all positive indices

$= \frac{1}{\cancel{t} u} \times \frac{\cancel{t}}{u} ^ 5 \times \frac{1}{t} ^ 4$

$= \frac{1}{{t}^{4} {u}^{6}}$

Jul 25, 2017

t^(-1)u^(-1)*tu^(-5)*t^-4u^0=1/(t^4u^6

#### Explanation:

${t}^{- 1} {u}^{- 1} \cdot t {u}^{- 5} \cdot {t}^{-} 4 {u}^{0}$

= $\left({t}^{- 1} \cdot {t}^{1} \cdot {t}^{-} 4\right) \cdot \left({u}^{- 1} \cdot {u}^{- 5} \cdot {u}^{0}\right)$

= ${t}^{- 1 + 1 + \left(- 4\right)} \cdot {u}^{- 1 + \left(- 5\right) + 0}$

= ${t}^{- 4} \cdot {u}^{- 6}$

= 1/(t^4u^6