Simplify:(9)1/3 × (27)1/2 / (3)1/6 × (3)-2/3
Solution:
Given, the expression is \(\frac{(9)^{\frac{1}{3}}\times (27)^{\frac{1}{2}}}{(3)^{\frac{1}{6}}\times (3)^{\frac{-2}{3}}}\)
We have to simplify the expression.
\((9)^{\frac{1}{3}}=(3^{2})^{\frac{1}{3}}=(3)^{\frac{2}{3}}\)
\((27)^{\frac{-1}{2}}=(3^{3})^{\frac{-1}{2}}=(3)^{\frac{-3}{2}}\)
We know \((a^{m})^{n}=a^{mn}\)
\((9)^{\frac{1}{3}}\times (27)^{\frac{-1}{2}}=(3)^{\frac{2}{3}}\times (3)^{\frac{-3}{2}}\)
We know \(a^{m}\times a^{n}=a^{m+n}\)
\((3)^{\frac{2}{3}}\times (3)^{\frac{-3}{2}}=(3)^{\frac{2}{3}+\frac{-3}{2}}=(3)^{\frac{-5}{6}}\)
\((3)^{\frac{1}{6}}\times (3)^{\frac{-2}{3}}=(3)^{\frac{1}{6}+\frac{-2}{3}}=(3)^{\frac{-3}{6}}\)
Now, \(\frac{(9)^{\frac{1}{3}}\times (27)^{\frac{1}{2}}}{(3)^{\frac{1}{6}}\times (3)^{\frac{-2}{3}}}\) = \(\frac{(3)^{\frac{-5}{6}}}{(3)^{\frac{-3}{6}}}\)
We know \(\frac{a^{m}}{a^{n}}=a^{m-n}\)
= \((3)^{\frac{-5}{6}-\frac{-3}{6}}\)
= \((3)^{\frac{-5}{6}+\frac{3}{6}}\)
= \((3)^{\frac{-5+3}{6}}\)
= \((3)^{\frac{-2}{6}}\)
= \((3)^{\frac{-1}{3}}\)
Therefore, the simplified expression is \((3)^{\frac{-1}{3}}\)
✦ Try This: simplify : \(\frac{(27)^{\frac{1}{3}}\times (9)^{\frac{1}{2}}}{(216)^{\frac{1}{6}}\times (3)^{\frac{-4}{3}}}\)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 14(v)
Simplify:(9)1/3 × (27)1/2 / (3)1/6 × (3)-2/3
Summary:
If r is a rational number and s is an irrational number, then r+s and r-s are irrationals. The simplified form of the expression is 3-⅓
☛ Related Questions:
visual curriculum