Writing Expression with Rational Exponents

• Rational exponents


  Exponents that are fractions
• Converting rational exponents to radicals

  1. Identify the base and exponent

  2. The denominator of the exponent becomes the index of the radical

  3. The numerator of the exponent becomes the power
• Converting radicals to rational exponents

  • (cube root of 5)^4
  • 6th root of 75 raised to 5
  • square root of 21 raised to 7
• Converting radicals to rational exponents

  1. The index of the radical becomes the denominator of the exponent

  2. The power becomes the numerator of the exponent
• Converting radicals to rational exponents

  • cube root of (x+2)
  • 2 raised to 1/4 power
  • cube root of m^2
• When converting between rational exponents and radicals, the base and power/index must be identified