Proof by Mathematical Induction - Example Proving Exponent Rule

This tutorial shows how mathematical induction can be used to prove a property of exponents.

Join this channel to get access to perks:

:)

[KR]

When using mathematical induction you shouldnt assume that the (k+1)th situation is correct. You should prove that it works by holding one side of equation and transforming that side using kth situation.

[denarandy]

hi your video helps me a lot!! I am stuck on combing K and K+1 exponents! can you do a video containing this?

[joaohax]

I think it's a weak way to show. I made it so:

We want to prove: (a^m)^n = a^(mn) for a, m, n in natural numbers such that a =/= 0 and m, n > 0

First step: show that it holds for the least case: n = 1

(a^m)^1 = a^(m.1)
a^m = a^m

Second step, we suppose that it works to a n = k

(a^m)^k = a^(m.k)

Third step: if it holds for n = k, then it must hold for n = k+1:
(a^m)^(k+1) = (a^m)(a^m)^k

(a^m)^k = a^(mk), as seen

so: (a^m)^(k+1) = a^mk . a^m = a^(mk+m) = a^(m(k+1))

(a^m)^(k+1) = a^(m(k+1))

Therefore, it's true that (a^m)^n = a^(mn) for a, m and n in natural numbers s.t a =/= 0 and m, n > 0

[laughingwhales]

Best Video I've seen yet on Mathematical Induction.
Very clear tutorial.

Thanks!

[getsetflyart]

Mad cycic teacher and then we will kill himself to be in touch and I am a bit more information on this one of my resume and I am a little more time with the new York NY times makes me know what I can get the best of the value your opinion about other people also I am not able Seaman book of the

[diedoktor]

Nice video! You forgot the last step where you substitute k with n though.

[Covidiousthenineteenth]

can you do a video on strong induction please?

[otakurocklee]

Poor presentation. You're doing the whole thing backwards which doesn't make sense.

You need to start with (a^(m))^k = a^(mk) and derive (a^m)^(k+1) = a^[m(k+1)].

You're starting with the final statement deriving the initial and then saying the final statement "had to be true".

[lancedaclizon]

can u make a video that answers dis quest...
find the integral solution : | x - 10| = 8
asap pls

[IbrahimEegan]

Can you prove matrix products using mathematical induction? :D

[BoZhaoengineering]

I remember this formula was presented in my 7 or 8th grade. I was taught to memorize the conclusion and not told the why it works by mathematical induction. I think there must be a missing proof for the formula.

[alittlefantastic]

Watching after 8 years..😄
Good class...

[erickmacias]

but then how do you prove that a^(x+y) = a^x a^y ?

[sadekomar]

I might be ignorant on something bigger that is happening over here, but this just looks like the begging the question (circular reasoning) fallacy to me.

[yisomabuza]

Can u try 💔 and explain thoroughly and sincerely cause ... u did a shoddy job 🙇🏾...

[DAVIDSTEPHENS]

A pretty lucid exposition! Importantly, the concept is explained.