Why are exponents efficient? All I know is they take up less room...?

Question

Can you give an example please, on how it would be easier than writing the whole number?

Answer 1

Consider the number "googol" (note this is not "Google"). The number googol is defined as a 1 followed by 100 zeros. Written out in ordinary form, it would look like this:

10,000,000,000,000,000,000,
000,000,000,000,000,000,000,
000,000,000,000,000,000,000,
000,000,000,000,000,000,000,
000,000,000,000,000,000
(that's all one number)

However, with exponential notation, we can write the same number much more efficiently:

10^100

Much easier, eh?

Answer 2

Would you rather write 4x4x4x4x4x4x4x4, 65536, or write 4^8? =)