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# What is a rational exponent notation?

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Rational or fractional exponents are another way of notating that some root of a base number should be taken, without using a radical sign. For instance, 16^1/2 is equivalent to taking the square root of 16, and 27^1/3 is equivalent to taking the cube root of 27.

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When using rational exponents, it is helpful to remember that the appropriate radical will undo an exponent. The cube root of 3^3 equals three, just as raising the cube root of 27 to the third power equals 27. Using rational exponents makes this relationship even clearer, because raising the cube root of 27 to the third power is written as (27^1/3)^3. When raising an exponent to another exponent, the answer is found by multiplying the exponents, so the problem can be rewritten 27^(1/3 x 3) or 27^1.

Rational exponents are often used in higher mathematics because they allow greater flexibility in manipulating complex exponential functions. For example, if called up on to multiply the square root of 4^3 times the cube root of 4^4, the whole expression could be written 4^3/2 x 4^4/3, which simplifies to 4^(3/2 x 4/3) or 4^2. When using rational exponents, always remember that the top number is the power, and the lower number is the root.

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