Answer :

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}

(225^{3})^{1/2} means ‘Cube of square root of 225’.

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

(2) (45)^{4/5}

(45^{4})^{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}

(81^{6})^{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}

(100^{4})^{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}

(21^{3})^{1/7} means ‘Cube of seventh root of 21’.

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

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