Solving a 'Harvard' University entrance exam question

Added: 2026-05-30

[00:00:00]Hello Friends find the value of 'a' If (√a√a√a√a)=7 let's have a solution so, we have a problem of (√a√a√a√a)=7 which can be solved by taking square on both sides ((√a√a√a√a))^2=(7)^2 as (√x)^2=x then It will be square cancels from square root we have a√a√a√a=7^2 now, to solve this, again take square on both sides (a(√a√a√a))^2=(7^2)^2 since (a^m)^n=a^(mn) then we have a^2.(√a√a√a)^2=7^4 by using this formula next, square cancels from square root a^2.a^1√a√a=7^4 as we know a^m.a^n=a^(m+n) by applying this formula we have a^3.√a√a=7^4 now, again take square on both sides (a^3.√a√a)^2=(7^4)^2 (a^3)^2.(√a√a)^2=7^8 next a^6.a√a=7^8 a^7.√a=7^8 again, take square on both sides (a^7)^2.(√a)^2=7^16 a^14.a^1=7^16 as we know a^15=7^16 to find 'a', take exponent (1/15) on both sides a^(15.1/15)=7^(16.1/15) 15 cancels we get the value of 'a' a=7^(16/15) thanks for watching this video please subscribe this channel to get the notification of my new videos ok bye