Question

simplify : 4th root of cube root of 2^2

Answer 1

Given: 4th root of cube root of 2^2

To find: Simplify the above term.

Solution:

• We have given 4th root of cube root of 2^2, means we can write it as:

           = $\sqrt[4]{\sqrt[3]{2^2} }$

• Which can be also written as:

           = (((2²)^1/3)^1/4

           = (2²)^1/12

• Now we know the formula: (a^m)^n = a^mn

• So applying this formula, we get:

           = (2)^(2 x 1/12)

           = (2)^1/6

Answer:

         So 4th root of cube root of 2^2 can be written as (2)^1/6.

Answer 2

Given: 4th root of cube root of 2^2

To find: Simplify the above term.

Solution:

We have given 4th root of cube root of 2^2, means we can write it as:

           =

Which can be also written as:

           = (((2²)^1/3)^1/4

           = (2²)^1/12

Now we know the formula: (a^m)^n = a^mn

So applying this formula, we get:

           = (2)^(2 x 1/12)

           = (2)^1/6

Answer:

         So 4th root of cube root of 2^2 can be written as (2)^1/6.

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