To simplify using exponents, one must express a number in the form a x 10^b, where b is your exponent. To do this, one must move the decimal point either to the right or to the left. Then, one counts how many place values the decimal point had moved; this is expressed as the exponent. For example, 19 000 000 can be simplified as 1.9 x 10^7. Lower numbers can also be simplified exponentially; for instance, 0.0000026 can be simplified as 2.6 x 10^-6.
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You can make it 4 to the 9th power and you will still get the same answer.
Exponents can simplify very ugly math problems and their relation to logarithms makes them invaluable. FYI logarithms were invented before exponents.
Exponents can be used to simplify notation when the same factor is repeated
419,854,000 using exponents is 4.19854 x 108
7,777 can be written as 7.78 × 103 using exponents.