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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