Mathematics » High School: Number & Quantity » The Real Number System

Extend the properties of exponents to rational exponents.

• 1. 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 5^1/3 to be the cube root of 5 because we want (5^1/3)³ = 5^(1/3)3 to hold, so (5^1/3)³ must equal 5.

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• 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

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Use properties of rational and irrational numbers.

• 3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

  Suggested tag: cc-9-12m-n-rn-3