Re: Exponents for exponents

If you are given:

$\displaystyle \left(4^{x+1} \right)^{x-1}$

then what you've done is correctly apply the property of exponents $\displaystyle (a^b)^c=a^{bc}$.

However, if you are given:

$\displaystyle 4^{(x+1)^{x-1}}$

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

Re: Exponents for exponents

The one I was given is the second one.

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

Re: Exponents for exponents

Quote:

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^x^{2}-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 $\displaystyle \left ( 2^3 \right ) ^4$ is not the same as $\displaystyle 2^{(3^4)}$

I will presume that the problem is $\displaystyle 4^{(x + 1) ^{x - 1}}$

So looking only at the exponent we have

$\displaystyle (x + 1)^{x - 1} = (x + 1)^x \cdot (x + 1)^{-1}$

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

Re: Exponents for exponents

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

4^{(x+1)^x * (x+1)^-1} = 4^{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.}