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# \(\sqrt[4]{\sqrt[3]{2^{2}}}\) equals

a. 2^{-1/6}

b. 2^{-6}

c. 2^{1/6}

d. 2^{6}

**Solution:**

Given

\(\sqrt[4]{\sqrt[3]{2^{2}}}\)

It can be written as

= [(2^{2})^{1/3}]^{1/4}

We know that [a^{m}]^{n} = a^{mn}

= (2^{2})^{1/12}

Similarly

= 2^{2 × 1/12}

= 2^{1/6}

Therefore, equals 2^{1/6}.

**✦ Try This: **\(\sqrt[5]{\sqrt[4]{3^{3}}}\) equals

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 1

**NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 17**

## \(\sqrt[4]{\sqrt[3]{2^{2}}}\) equals a. 2^{-1/6}, b. 2^{-6}, c. 2^{1/6}, d. 2^{6}

**Summary**:

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). So it is equal to 2^{1/6}

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