Access Point #: MAFS.912.N-RN.1.AP.1a (Archived Access Point)


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Understand that the denominator of the rational exponent is the root index and the numerator is the exponent of the radicand (e.g., 51/2 = √5). Extend the properties of exponents to justify that (51/2)2=5

Clarifications:

Essential Understandings

Concrete:

  • Identify a fractional exponent.
  • Use manipulatives to demonstrate laws of exponents.
Representation:
  • Understand the following concepts, symbols and vocabulary: radicand, root index, root, numerator, denominator, radical, exponent.
  • Understand the parts of a fraction.
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  • Understand how to multiply fractions and whole numbers.
  • Understand that a fractional exponent is a root.
  • Understand that a root is the inverse of a fractional exponent.
  • Understand that “radicals” (roots) are the “opposite” operation of applying exponents.
  • Understand that you can “undo” a power with a radical, and a radical can “undo” a power.

Number: MAFS.912.N-RN.1.AP.1a Category: Access Points
Date Adopted or Revised: 07/14 Cluster: Extend the properties of exponents to rational exponents. (Algebra 1 - Major Cluster) (Algebra 2 - Major Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Related Standards

Name Description
MAFS.912.N-RN.1.1: 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  to be the cube root of 5 because we want  = to hold, so must equal 5.



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