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

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.
  • 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.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.
  • MII.A-SSE.B.3.c
    Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.15 1/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
  • MII.F-IF.C.8.b
    Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as Identifying appreciation/depreciation rate for the value of a house or car some time after its initial purchase: Vn=P(1+r)n. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2) t /10, and classify them as representing exponential growth or decay.
  • MIII.A-REI.A.2
    Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.