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Mathematics > Course Model Mathematics II (Integrated Pathway) > The Real Number System
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - The Real Number System

Cluster - Extend the properties of exponents to rational exponents.

[MII.N-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. 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.

Resources:


  • Exponent
    The number that indicates how many times the base is used as a factor, e.g., in 43 = 4 x 4 x 4 = 64, the exponent is 3, indicating that 4 is repeated as a factor three times.
  • Integer
    All positive and negative whole numbers, including zero.
  • Radical
    The √ symbol, which is used to indicate square roots or n th roots.
  • Rational number
    A number expressible in the form a∕b or – a∕b for some fraction a∕b. The rational numbers include the integers.

Predecessor Standards:

  • 8.EE.A.1
    Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² x 3-5 = 3-3 = 1/33 = 1/27.
  • 8.EE.A.2
    Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Successor Standards:

No Successor Standards found.

Same Level Standards:

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