![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Prove that:$ \sqrt{\frac{1}{4}}+(0.01)^{-1 / 2}-(27)^{-2 / 3}=\frac{3}{2} $
Given:
\( \sqrt{\frac{1}{4}}+(0.01)^{-1 / 2}-(27)^{-2 / 3}=\frac{3}{2} \)
To do:
We have to prove that \( \sqrt{\frac{1}{4}}+(0.01)^{-1 / 2}-(27)^{-2 / 3}=\frac{3}{2} \).
Solution:
We know that,
$(a^{m})^{n}=a^{m n}$
$a^{m} \times a^{n}=a^{m+n}$
$a^{m} \div a^{n}=a^{m-n}$
$a^{0}=1$
Therefore,
LHS $=\sqrt{\frac{1}{4}}+(0.01)^{\frac{-1}{2}}-(27)^{\frac{2}{3}}$
$=(\frac{1}{2^{2}})^{\frac{1}{2}}+(0.1)^{2 \times(\frac{-1}{2})}-(3^{3})^{\frac{2}{3}}$
$=\frac{1}{(2^{2})^{\frac{1}{2}}}+(0.1)^{2 \times(\frac{-1}{2})}-3^{3 \times \frac{2}{3}}$
$=\frac{1}{2^{1}}+(0.1)^{-1}-3^{2}$
$=\frac{1}{2}+(\frac{1}{10})^{-1}-3^{2}$
$=\frac{1}{2}+10-9$
$=\frac{1}{2}+1$
$=\frac{3}{2}$
$=$ RHS
Hence proved.
Advertisements