They are used as an easy, convenient way to express very large and very small numbers.
Examples:
Charge on one electron = [ 0.0000000000000000001602 Coulomb ] or [ 1.602 x 10-19 Coulomb ]
One light-year: [ 5,878,700,000,000 miles ] or [ 5.8787 x 1012 miles ].
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It certainly has a meaning. It is only meaningless if you consider powers as repeated multiplication; but the "extended" definition, for negative and fractional exponents, makes a lot of sense, and it is regularly used in math and science.
They are not. Exponents, powers and indices are terms used for the same thing.
This exact question is on a puzzle worksheet over rational exponents used by teachers. The answer to the puzzle is Nicole Oresme.
The rule is that you multiply the exponents. So if I have 2 squared and I want to raise it to the third power, you multiply the 2x3=6. When you multiply powers you add the exponents. When you raise exponents to a power you multiply. This works for rational exponents which can be used to represent roots as well.
you do not do anything when you add numbers with exponents. you just figure out the answer. it is only if you multiply numbers with exponents, where you add the exponents..