Question

Question #5fc4b

Answer 1

Do `(8.03)^-4` and `(10^4)^-4`separately, then use exponent properties

Explanation:

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

Exponent properties:

`(ab)^n = a^n \cdot b^n`
`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}`