Question

Write the following numbers in the form of rational indices.(1) Square root of 5th power of 121. (2) Cube of 4th root of 324(3) 5th root of square of 264 (4) Cube of cube root of 3

Answer 1

Hi,

Question:Write the following numbers in the form of rational indices.(1) Square root of 5th power of 121. (2) Cube of 4th root of 324(3) 5th root of square of 264 (4) Cube of cube root of 3

Solution:

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

= $(121)^{\frac{5}{2}}$

(2) Cube of 4th root of 324:

= $(324)^{\frac{3}{4}}$

(3) 5th root of square of 264:

= $(264)^{\frac{2}{5}}$

(4) Cube of cube root of 3:

= $(3)^{\frac{3}{3}}$

hope it helps you.

Answer 2

We can write the following numbers in the form of rational indices as follows:

1) square root of 5th power of 121 can be written as (121^5)^(1/2)

2)Cube of 4th root of 324 can be written as (324^(1/4))^3

(3) 5th root of square of 264 can be written as (264^2)^(1/5)

(4) Cube of cube root of 3 can be written as (3^(1/3))^3; solving it we'll get 3 as answer.