One use is shorthand for large numbers, eg the mass of the earth is
5960000000000000000000000 kg , which can be expressed as:
5.96 * 1024 kg
there are also rules for multiplying / dividing exponential numbers
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Math
A carpenter won't usually have much use for exponents, or other advanced math topics.
All the powers and exponents of 1 are 1.The powers and exponents of any of the other numbers up to 10 are equivalent to the all the positive numbers - rational and irrational.
other subjects in school dumbo
A rational exponent means that you use a fraction as an exponent, for example, 10 to the power 1/3. These exponents are interpreted as follows, for example:10 to the power 1/3 = 3rd root of 1010 to the power 2/3 = (3rd root of 10) squared, or equivalently, 3rd root of (10 squared)