![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
Simplify:
$ \frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}} $
Given:
\( \frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}} \)To do:
We have to simplify \( \frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}} \).
Solution:
We know that,
$a^{-m}=\frac{1}{a^m}$
$a^m \times a^n=a^{m+n}$
$a^{m}\div a^{n}=a^{m-n}$
Therefore,
$\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}=\frac{3^{-5} \times (5\times2)^{-5} \times 5^3}{5^{-7} \times (2\times3)^{-5}}$
$=\frac{3^{-5} \times 5^{-5} \times 2^{-5} \times 5^3}{5^{-7} \times 2^{-5}\times3^{-5}}$
$=2^{-5+5}\times3^{-5+5}\times5^{-5+3+7}$
$=2^0\times3^0\times5^5$
$=1\times1\times5^5$
$=5^5$
Hence, $\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}=5^5$.
Advertisements