Complete the following table.

Explanation of Table

Generally we can express two meaning of the number a^m/n.

a^m/n = (a^m)^1/n means ‘n^th root of m^th powerof a’.

a^m/n = ()^m means ‘m^th power of n^th root of a’.

(1) (225)^3/2

(225³)^1/2 means ‘Cube of square root of 225’.

(225^1/2)³ means ‘Square root of cube of 225’.

(2) (45)^4/5

(45⁴)^1/5 means ‘Fourth power of fifth root of 45’.

(45^1/5)⁴ means ‘Fifth root of fourth power of 45’.

(3) (81)^6/7

(81⁶)^1/7 means ‘Sixth power of seventh root of 81’.

(81^1/7)⁶ means ‘Seventh root of sixth power of 81’.

(4) (100)^4/10

(100⁴)^1/10 means ‘Fourth power of tenth root of 100’.

(100^1/10)⁴ means ‘Tenth root of fourth power of 100’.

(5) (21)^3/7

(21³)^1/7 means ‘Cube of seventh root of 21’.

()³ means ‘Seventh root of cube of 21’.