Question

(3.2 * 10000000) -3

Answer 1

The exponents distribute over factors:

`(ab)^c = a^c * b^c`

so, you have

`(3.2 * 10^6)^(-3) = 3.2^(-3) * (10^6)^(-3)`

Let's focus on each factor: applying the definition of negative exponents, you have

`3.2^(-3) = \cfrac{1}{3.2^3} \approx 0.03`

While for the power of 10, you can use the following rule

`(a^b)^c = a^(bc)` to write

`(10^6)^(-3) = 10^(6\cdot (-3)) = 10^(-18)`

So, the expression evaluates to

`0.03* 10^(-18) = 3* 10^(-20)`