Why are the exponents decreasing?

Question

My geology teacher did a problem with us,  and I get everything but why did the exponent 27 decrease to 21, then to 16? I didn't notice while I was in class. :/

 

Calculate the Volume of the Earth.

4/3 x π x r3
V = .75 x 3.1415 x 637 13
V = 15010872.375 km3

Density - mass/volume

D = 5.98 x 10^27g/15010872.375 km3
D = 3.98 x 10^21 g/km3
D = 3.98 x 10^16 g/cm3

Answer 1

The earth volume math is incorrect.  Instead of

 

V = 0.75 x 3.1415 x 6371³ km³

 

it should say

 

V = (4/3) x  3.1416 x (6371)³ km³ ≅ 1.0832 x 10¹² km³

 

Also, recall that

 

1 km = 1000 m = 1000 x 100 cm = 100,000 cm

 

1 km³ = 100,000³ cm³

 

Use this when you convert volume from km³ to cm³.