Question #5fc4b

1 Answer
Jan 3, 2018

Answer:

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}#