# Question #5fc4b

Jan 3, 2018

Do ${\left(8.03\right)}^{-} 4$ and ${\left({10}^{4}\right)}^{-} 4$separately, then use exponent properties

#### Explanation:

${\left(8.03 \setminus \times {10}^{4}\right)}^{- 4}$

Exponent properties:

${\left(a b\right)}^{n} = {a}^{n} \setminus \cdot {b}^{n}$
${a}^{n} \setminus \cdot {a}^{m} = {a}^{n + m}$

Scientific notation is just multiplication, so we use exponent property

$\setminus q \quad {\left(8.03 \setminus \times {10}^{4}\right)}^{- 4} = {8.03}^{- 4} \setminus \times {\left({10}^{4}\right)}^{- 4}$

On a calculator, ${8.03}^{- 4}$ gets me $0.0002405$, which is equivalent to $2.405 \setminus \times {10}^{- 4}$.

And ${\left({10}^{4}\right)}^{- 4} = {10}^{- 16}$.

$\setminus q \quad \left(2.405 \setminus \times {10}^{- 4}\right) \setminus \times {10}^{- 16} = 2.405 \setminus \times {10}^{- 4 - 16}$

$\setminus q \quad = 2.405 \setminus \times {10}^{- 20}$