Simplify. Write each answer in scientific notation.

15. (6 ˣ 10^-5) ^3

19. 3 ˣ 10^-2 / 8 ˣ 10^-1

20. 4.1 ˣ 10^-4 / 1.28 ˣ 10^-5

21. 1.91 ˣ 10^3 / 5 ˣ 10^-4

Scientific notation is always supposed to be

(a number between 1 and 10) x 10^whatever power.

15. (6 x 10⁻⁵) ³

The 'cube' works on everything inside the parentheses ...

the 6 and the 10⁻⁵.

So this thing is (6) ³ x (10⁻⁵) ³.

That's (216) x (10⁻¹⁵). After cleaning up, it's 2.16 x 10⁻¹³.

19. 3 ˣ 10⁻² / 8 ˣ 10⁻¹

This mess can be written in a slightly different way,

and it may be clearer to you that way:

(3/8) x (10⁻²/10⁻¹)

The 3/8 is 0.375.

The second factor is 10⁻¹.

So we have 0.375 x 10⁻¹. After cleanup, it's 3.75 x 10⁻².

20. 4.1 ˣ 10⁻⁴ / 1.28 ˣ 10⁻⁵

Write it like this: (4.1/1.28) x (10⁻⁴/10⁻⁵)

The first part is 4.1/1.28 = 3.203125.

The second part is (10⁻⁴/10⁻⁵) = 10¹

So it boils down to 3.203125 x 10¹.

21. 1.91 ˣ 10³ / 5 ˣ 10⁻⁴

Write it like this: (1.91/5) x (10³/10⁻⁴)

First part: 1.91/5 = 0.382

Second part: (10³/10⁻⁴) = 10⁷

Put um together: 0.382 x 10⁷. After cleanup: 3.82 x 10⁶.