Question #5fc4b

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Answer 1 · 2018-01-03T19:35:41

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

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

Exponent properties:

${(a b)}^{n} = a^{n} \cdot b^{n}$ $(ab)^n = a^n \cdot b^n$
$a^{n} \cdot a^{m} = a^{n + m}$ $a^n \cdot a^m = a^{n+m}$

Scientific notation is just multiplication, so we use exponent property

$\qquad (8.03\times 10^4)^{-4} = 8.03^{-4} \times(10^4)^{-4}$

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

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

$\qquad (2.405\times 10^{-4}) \times 10^{-16} = 2.405 \times 10^{-4 -16}$

$\qquad =2.405 \times 10^{-20}$