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Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = 5 to the (1/3)(3) power to hold, so (5 to the 1/3 power)³ must equal 5.