Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
6.2k views
in Exponents by (30.2k points)
closed by

If a, m, n are positive integers, then \(\{m\sqrt{n\sqrt{a}}\}^{mn}\) is equal to

A. amn

B. a

C. am/n

D. 1

1 Answer

+1 vote
by (28.9k points)
selected by
 
Best answer

\(\{m\sqrt{n\sqrt{a}}\}^{mn}\)

We know for any non-zero number a,

am × an = am+n

\(\{(a^{\frac{1}{n}})^{\frac{1}{m}}\}^{mn}\)

Again using (am)n = amn we get, = \(\{a^{\frac{1}{mn}}\}^{mn}\) = a

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...