# High School: Number and Quantity » The Real Number System

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#### Extend the properties of exponents to rational exponents.

CCSS.Math.Content.HSN.RN.A.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.

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 5CCSS.Math.Content.HSN.RN.A.2

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

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

#### Use properties of rational and irrational numbers.

CCSS.Math.Content.HSN.RN.B.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.

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.