Why are there exponents?

Answer 1

Exponents (sometimes called powers or indices - the plural of index) are a simple and easy notation, and they save a lot of time. For exampe, say you wanted to write out a googol in full; that is, 10100. * Which is easier to do: that exponent, or 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10? * Another example is the opposite: 10-60, or 0.0000000000000000000000000000000000000000000000000000000000001? So exponents make life very easy for mathematicians, physicists, chemists, engineers and many other people that have to deal with large numbers on a regular basis. Another effect of using exponents is that multiplication is also easier. For 211 x 218, rather than work out 218 and 211 and then mulitply those large numbers together, we can simply add the exponents and then calculate the final result, i.e. 229 (which for the record, is 536870912). The opposite works for division as well; simply subtract the exponents to get the divided amount. They can be used in many other ways as well to make working very large or very small numbers much easier.