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In this 10th grade math lesson, students simplifying rational exponents. This lesson includes four worksheets of varying levels with 12 problems each and an answer key included. It also includes an optional homework assignment, also 12 problems.
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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.