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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
1.13 Fractional or Rational Exponents

Radicals (square roots, cube roots, fourth root etc) or Fractional exponents
  • A fractional exponent like 1/n means to take the nth root
    nx = x1/n
  • Number to power of half is the square root
    4 = 41/2
  • Number to the power of 1/3 is the cube root
    38 = 81/3
  • Number to the power of 1/4 is the fourth root
    416 = 161/4
  • In a fractional exponent, the top number is the power, and the lower number is the root.
    Example:
    82/3
    In the fractional exponent 2/3, 2 is the power and 1/3 is the cube root
    we can either find the cube root of 8 first or square 8 first
    (81/3)2 = 22 = 4
    (82)1/3 = 364 = 4
  • Decimal powers can be written as fractional exponents.
    Example:
    40.5 = 41/2 = 2
  • Do not write square root of a negative number.
    Example:
    -4
    They are expressed as complex numbers.

Directions: Answer the following questions. Also write at least ten examples for fractional exponents - square roots, cube roots, fourth root and decimal exponents.
Q 1: Find the value for the exponent: (80)5 =
Answer:

Q 2: Find the value for the exponent: 81/3 =
Answer:

Q 3: Find the value for the exponent: 5121/3 =
Answer:

Q 4: Find the value for the exponent: 42.5 =
Answer:

Q 5: Find the value for the exponent: 645/6 =
Answer:

Q 6: Find the value for the exponent: 811/2 =
Answer:

Q 7: Find the value for the exponent: 40961/6 =
Answer:

Q 8: Find the value for the exponent: 271/3 =
Answer:

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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