A fractional exponent like 1/n means to take the nth root
nÖx = x^{1/n}
Number to power of half is the square root
Ö4 = 4^{1/2}
Number to the power of 1/3 is the cube root
3Ö8 = 8^{1/3}
Number to the power of 1/4 is the fourth root
4Ö16 = 16^{1/4}
In a fractional exponent, the top number is the power, and the lower number is the root.
Example: 8^{2/3}
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
(8^{1/3})^{2} = 2^{2} = 4
(8^{2})^{1/3} = 3Ö64 = 4
Decimal powers can be written as fractional exponents.
Example:
4^{0.5} = 4^{1/2} = 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.