# Question #34e81

May 21, 2016

I hope it helps:

#### Explanation:

The good thing about scientific notation is that you do not need to deal with a lot of zeros and the operations are quite simplified. The problem is that you need to remember some rules of exponents!
In your case you have a multiplication that can be written as:
$\left(8.2 \cdot 2.1\right) \cdot \left({10}^{2} \cdot {10}^{5}\right) =$
here you take advantage of the fact that the order in the multiplication is irrelevant.

The first multiplication is easy to do while the second can be solved remembering that: ${x}^{m} \cdot {x}^{n} = {x}^{m + n}$

so, basically, if the base is the same ($10$) you simply add the exponents:
${10}^{2} \cdot {10}^{5} = {10}^{2 + 5} = {10}^{7}$
your number then becomes:
$\left(8.2 \cdot 2.1\right) \cdot \left({10}^{2} \cdot {10}^{5}\right) = 17.22 \cdot {10}^{7}$ or $1.722 \cdot {10}^{8}$

Consider a division now and see, by yourself, what will be the result!