Write the following number in the form of rational indices.

(1) Square root of 5^th power of 121.

(2) Cube of 4^th root of 324.

(3) 5^th root of square of 264.

(4) Cube of cube root of 3.

we know that ‘n^th root of m^th powerof a’ is expressed as (a^m)^1/n

and ‘m^th power of n^th root of a’ is expressed as ()^m.

(1) Square root of 5^th power of 121.

We know that,

‘n^th root of m^th powerof a’ is expressed as (a^m)^1/n

So, ‘Square root of 5^th power of 121’ is expressed as (121⁵)^1/2 or (121)^5/2.

(2) Cube of 4^th root of 324.

We know that,

‘n^th root of m^th powerof a’ is expressed as (a^m)^1/n

So, ‘Cube of 4^th root of 324’ is written as (324^1/4)³ or (324)^3/4.

(3) 5^th root of square of 264.

We know that,

‘n^th root of m^th powerof a’ is expressed as (a^m)^1/n

So, ‘5^th root of square of 264’ is written as (264²)^1/5 or

(264)^2/5.

(4) Cube of cube root of 3.

We know that,

‘m^th power of n^th root of a’ is expressed as ()^m

So, ‘Cube of cube root of 3’ is written as (3^1/3)³ or (31)^3/3.