Scientific notation help!!?

Question

how would you solve this?

(1.2 * 10^ -3)^2 divided by (10^-2)^3 *(2.0 * 10^3)

thanks!!

Answer 1

(1.2 * 10^ -3)^2 divided by (10^-2)^3 *(2.0 * 10^3)

OK. When multiplying exponents:
a^x + a^y = a^(x+y)
And (a * b^x)y = a^y * b^(x*y)
So:
(1.2 * 10^3)^2 = 1.44 * 10^6 (numerator)
and
(10^-2)^3 *(2.0 * 10^3) = 10^-6 * 2.0 * 10^3 = 2.0 * 10^-3 (denominator)

Your fraction is then:
(1.44 * 10^6) / 2.0 * 10^3) which can be split into:
1.44 / 2.0 * 10^6/10^3 = .72 * 10^3

For scientific notation, you need to make the first part greater than 1, so:
.72 * 10 * 10^3 * 1/10 = 7.2 * 10^2