# Exponents for exponents

• Sep 24th 2012, 10:30 AM
JrAl
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.
• Sep 24th 2012, 10:38 AM
MarkFL
Re: Exponents for exponents
If you are given:

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

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

However, if you are given:

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

then there isn't much you can do to simplify that I know of.
• Sep 24th 2012, 10:46 AM
JrAl
Re: Exponents for exponents
The one I was given is the second one.

I'm thinking of basing it on am*an=am+n and a-n=1/an but can't seem to figure it out.
• Sep 24th 2012, 10:46 AM
topsquark
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^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 $\left ( 2^3 \right ) ^4$ is not the same as $2^{(3^4)}$

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

So looking only at the exponent we have
$(x + 1)^{x - 1} = (x + 1)^x \cdot (x + 1)^{-1}$

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
• Sep 24th 2012, 11:03 AM
JrAl
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 = 41/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.