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# Simplify: \([5(8^{\frac{1}{3}}+27^{\frac{1}{3}})^{3}]^{\frac{1}{4}}\)

**Solution:**

Given, the expression is \([5(8^{\frac{1}{3}}+27^{\frac{1}{3}})^{3}]^{\frac{1}{4}}\)

We have to simplify the expression.

= \([5((2^{3})^{\frac{1}{3}}+(3^{3})^{\frac{1}{3}})^{3}]^{\frac{1}{4}}\)

By further simplification

= \([5(2+3)^{3}]^{\frac{1}{4}}\)

So we get

= \([5(5)^{3}]^{\frac{1}{4}}\)

= \([5^{4}]^{\frac{1}{4}}\)

= 5

Therefore, \([5(8^{\frac{1}{3}}+27^{\frac{1}{3}})^{3}]^{\frac{1}{4}}=5\)

**✦ Try This: **Simplify : \((12(216^{\frac{1}{3}}+8^{\frac{1}{3}})^{3})^{\frac{1}{4}}\)

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

**NCERT Exemplar Class 9 Maths Exercise 1.3 Sample Problem 5**

## Simplify: \((5(8^{\frac{1}{3}}+27^{\frac{1}{3}})^{3})^{\frac{1}{4}}\)

**Summary:**

Fractions are made up of whole numbers while rational numbers are made up of integers as their numerator and denominator. The simplified form is 5

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