Why is a rational exponent an exponent in the form of a fraction?

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A rational exponent is an exponent in form of a fraction because by definition, rational numbers are numbers that could be written as "ratios", or fractions.

This includes, obviously, fractions, such as 3/5 or 13/4, decimals (they could be converted into fractions) and integers (they could be written as fractions with the denominator 1:  5 = 5/1). All these can be positive or negative.

An example of a number that is NOT rational would be `sqrt2` , because it cannot be converted into a fraction. If you plug `sqrt2` in a calculator, you will see that this is a decimal which has infinite number of digits after the decimal point, not arranged in any kind of pattern. Such numbers are called "irrational".

So, rational exponent just means that the exponent is a rational number.

 

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