Exponents for exponents

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September 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.
September 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.
September 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 a^m*aⁿ=a^m+ⁿ and a^-n=1/aⁿ but can't seem to figure it out.
September 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
September 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} = 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.}