# How to simplify (7.87 times 10^-1)^-6  in scientific notation?

Jun 8, 2016

${\left(7.87 \times {10}^{- 1}\right)}^{- 6} = 4.2087$

#### Explanation:

As ${a}^{- m} = \frac{1}{a} ^ m$, ${\left(a b\right)}^{n} = {a}^{n} \times {b}^{n}$, ${\left({a}^{m}\right)}^{n} = {a}^{m \times n}$ and ${\left(\frac{a}{b}\right)}^{n} = {a}^{n} / {b}^{n}$

${\left(7.87 \times {10}^{- 1}\right)}^{- 6}$

= ${7.87}^{- 6} \times {\left({10}^{- 1}\right)}^{- 6}$

= $\frac{1}{7.87} ^ 6 \times {10}^{\left(- 1\right) \times \left(- 6\right)}$

= $\frac{1}{237601.07} \times {10}^{6}$

= $\frac{1000000}{237601.07}$

= $4.2087$