Fractional Indices

Fractional Indices

({a^{frac{1}{n}}}) is a nth root of a. [{a^{frac{1}{n}}} = sqrt[n]{a}] ({a^{frac{m}{n}}}) means the nth root of ({a^m}).
a m n = a m n
Example:
Find the value of the following:
a. ({81^{frac{1}{2}}})
b. ({64^{frac{1}{3}}})
c. ({625^{frac{1}{4}}})
Answer:
a.
[{81^{frac{1}{2}}} = sqrt {81} = 9]
b.
[{64^{frac{1}{3}}} = sqrt[3]{{64}} = 4]
c.
[{625^{frac{1}{4}}} = sqrt[4]{{625}} = 5]

Example:
Find the value of the following:
a. ({16^{frac{3}{2}}})
b. ({left( {frac{{27}}{{64}}} right)^{frac{2}{3}}})
Answer:
a.
16 3 2 = ( 16 ) 3 = 4 3 =64
b.
( 27 64 ) 2 3 = ( 27 64 3 ) 2 = ( 3 4 ) 2 = 9 16

Leave a Reply

Your email address will not be published. Required fields are marked *