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### Grade 7 - Mathematics3.6 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 nÖx = x1/n Number to power of half is the square root Ö4 = 41/2 Number to the power of 1/3 is the cube root 3Ö8 = 81/3 Number to the power of 1/4 is the fourth root 4Ö16 = 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 = 3Ö64 = 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: Ö-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: 31251/5 = Answer: Q 2: Find the value for the exponent: 81/3 = Answer: Q 3: Find the value for the exponent: 43/2 = Answer: Q 4: Find the value for the exponent: 161/2 = Answer: Q 5: Find the value for the exponent: 40961/6 = Answer: Q 6: Find the value for the exponent: 24011/4 = Answer: Q 7: Find the value for the exponent: 271/3 = Answer: Q 8: Find the value for the exponent: 42.5 = Answer: Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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