Standards in this domain:

• N-RN.1
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• N-RN.2
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• N-RN.3

Extend the properties of exponents to rational exponents.

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

Use properties of rational and irrational numbers.

• N-RN.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.