N.RN.1: Understanding Rational Exponents through the Extension of Integer Exponents Properties
Grade: Number & Qty
Domain: RN: The Real Number System
Standard Description
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 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
Domain Description
The concept of rational exponents essentially comes from expanding the rules of integer exponents, creating a way to express radicals. As an instance, we establish 51/3 as the cube root of 5 to maintain equality in the equation (51/3)3 = 5.
It's possible to transcribe equations with radicals and rational exponents by utilising exponent laws.
The resultant of adding or multiplying two rational numbers is always rational; however, if a rational number is added or multiplied to an irrational number, the outcome remains irrational.