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 .

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