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Fractional Exponents
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Fractional Exponents:
Exponent means how many times a number is repeated in multiplication.
A fraction having exponent form and following rules which is followed by the integers.
A fractional exponents form is 1/n. Fractional exponents can be used instead of using the radical sign ().
General Formula of Fractional Exponent:
The n-th root of a number can be written using the power 1/n, as follows:
       a1/n = na
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Example: If y = 31/3 + 1/(31/3), show that 3y3 - 9y = 10.
Solution: Let a = 31/3Then a3 = 3      .......(i)
and b = 1/(31/3) Then b3 = 1/3          .......(ii)
Also, ab = [31/3] [1/(31/3)] = 1          .......(iii)
a + b = y                                          ......(iv)
y = 31/3 + 1/(31/3) = a + b
y3 = (a + b)3 = a3 + b3 + 3ab(a + b)
Using (i), (ii), (iii) and (iv) here, you get
y3 = 3 + 1/3 + 3(1)(y)

Multiplying both sides with 3, you get
        3y3 = 9 + 1 + 9
     3y3 - 9y = 10.(Proved.)
 
   
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