In the first part of this example, you have:

(405 nm/1) x (10^-9 m/1nm)

When you multiply 405 by 10^-9, you get

405 x 10^-9

This is not standard scientific notation, because there is no decimal place in 405. To get it into scientific notation, move the decimal to the left 2 places. This decreases 405 by a factor of 100. To keep the value of the entire number the same, then, you must INCREASE 10^-9 by 100. Increasing 10^-9 by 100 gives you 10^-7. Thus, it is 4.05 x 10^-7 m.

In the next step, you have

(3.0 x 10⁸ m/s) / (4.05 x 10^-7 m)

You can divide the two numbers first:

3.0 / 4.05 = 0.74

You can then divide the two exponents. When multiplying numbers with exponents, you ADD the exponents. When dividing numbers with exponents, you SUBTRACT the exponents:

10⁸ / 10^-7 = 10^{(8 – -7)} = 10¹⁵

Thus, you have an answer of 0.74 x 10¹⁵. Once again, this is not standard scientific notation. To get it into standard scientific notation, multiply 0.74 by 10 to get 7.4. This means you must divide 10¹⁵ by 10 to get 10¹⁴. Thus, the answer is:

7.4 x 10¹⁴ 1/s

Now, having done all that, if you have a scientific calculator, it allows you to input the numbers in scientific notation and it does all of this for you. If you have a scientific calculator, read the manual to find out how to do this or you might be able to find a YouTube video explaining how to do it.