# How do you simplify (4 times 10^13)^-2 and write the answer in scientific notation?

Jun 11, 2016

${\left(4 \times {10}^{13}\right)}^{- 2} = 6.25 \times {10}^{- 28}$

#### Explanation:

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

${\left(4 \times {10}^{13}\right)}^{- 2}$

= ${4}^{- 2} \times {\left({10}^{13}\right)}^{- 2}$

= $\frac{1}{4} ^ 2 \times {10}^{- 26}$

= $\frac{1}{2} ^ 4 \times {10}^{- 26}$

= $\frac{1 \times {5}^{4}}{{2}^{4} \times {5}^{4}} \times {10}^{- 26}$

= $\frac{625}{10} ^ 4 \times {10}^{- 26}$

= $625 \times {10}^{- 30}$

= $6.25 \times {10}^{- 28}$, which is in scientific notation.