Test 7.6-7.7

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7.6: Rational Exponents

  • convert rational exponent into roots and back again
  • evaluate with rational exponents
  • simplifying with rational exponents
  1. leave in rational form
  2. all positive exponents
  3. exponents in denominators must be positive integers (may need to rationalize denominator)
    • rationalize by multiplying by roots or fractional powers
    • rationalize by multiplying with the conjugate

7.7: Solving Radical Equations and Inequalities

  • solve for the variable and check if the answer is an extraneous solution
  • use inverses: roots (and fractional powers) are inverses of powers
  • solve radical inequalities
    • hidden inequalities from the even roots
    • solve for the variable in all inequalities
    • all inequalities must be satisfied: "and"
    • visualize and test answer with a number line
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