Thread: Exponents for exponents

Hi,

I just stumbled on a problem in my math work.

My job is to simplify/reduce the following exponentiation:
4^(x+1)^x-1

My solution for it is following:

4^(x+1)^x-1​ = 4^(x+1)(x-1) = 4^x²-1

But I got a feeling, that it's wrong. So I want to know, what I'm doing wrong.

Thanks.

If you are given:



then what you've done is correctly apply the property of exponents .

However, if you are given:



then there isn't much you can do to simplify that I know of.

The one I was given is the second one.

I'm thinking of basing it on a^m*aⁿ=a^m+ⁿ and a^-n=1/aⁿ but can't seem to figure it out.

Originally Posted by JrAl

Hi,

I just stumbled on a problem in my math work.

My job is to simplify/reduce the following exponentiation:
4^(x+1)^x-1

My solution for it is following:

4^(x+1)^x-1​ = 4^(x+1)(x-1) = 4^x²-1

But I got a feeling, that it's wrong. So I want to know, what I'm doing wrong.

Thanks.

First there is the matter of notation. Please note that is not the same as

I will presume that the problem is

So looking only at the exponent we have


If you need more, let us know.

I'm rather curious about this. I can see no way to put the original expression into something that it can be reduced to.

-Dan

I've tried working with the tip (thanks), and my current result is the following:

4^{(x+1)^x * (x+1)^-1} = 4<sup>1/x+1^(-x) * 1/x+1

Again, am I not sure, if I'm doing it right. So it would be nice with a little more.</sup>