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US-AK

Math

Alaska Math

Number and Quantity: The Real Number System

Extend the properties of exponents to rational exponents.

N-RN.1

Fully covered
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

Mostly covered
Rewrite expressions involving radicals and rational exponents using the properties of exponents. For example: Write equivalent representations that utilize both positive and negative exponents.

Use properties of rational and irrational numbers.

N-RN.3

Fully covered
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.