Simplify Indices Equations to Solving Math Homework

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Hi!I have got problem on Indices ( which i think i 'm not nearing any solution )

Homework Statement

Well the sum is

a ^{m^n}= (a ^m)ⁿ
Now it is to be expressed in terms of n

Homework Equations

none

The Attempt at a Solution

I tried this way
as the bases are same
.: m ⁿ= m x n
=m ^n-1=n
(is this going to go any further??)

I would be very happy if anyone helped.!
Thanks!

 

[Mark44]

Hi!I have got problem on Indices ( which i think i 'm not nearing any solution )

Homework Statement

Well the sum is

a ^{m^n}= (a ^m)ⁿ

This is incorrect, and it is not a sum. You have a sum when you add expressions.

Let's look at an example to make things more concrete.

2³⁴ = 2⁸¹
(2³)⁴ = 8⁴ = 4096 = 2¹². Clearly the two expressions above are unequal.

In general, a^mn \neq (a^m)ⁿ.
BTW, in English what you are calling an index, we would call an exponent.

Now it is to be expressed in terms of n

Homework Equations

none

The Attempt at a Solution

I tried this way
as the bases are same
.: m ⁿ= m x n
=m ^n-1=n
(is this going to go any further??)

It shouldn't go even this far. mⁿ \neq m x n, and m^{n - 1} \neq n. I can't even tell what you're trying to do here.

I would be very happy if anyone helped.!
Thanks!

 

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Actually by sum I mean 'problem'.