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Exponential functions

linapril

New member
Dec 21, 2012
23
Hello! Could someone please help me answer this question, and explain how you answered it?

1. (x1/2 + x-1/2)2


​Thank you!
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,197
What are you asked to do? And what steps have you made towards doing that?
 

linapril

New member
Dec 21, 2012
23
It just says to simplify it.
I multiplied away the brackets, getting x + x, which equals 2x. But this answer's wrong apparently...
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,197
Yes, there are several errors in your computations. The first error, seemingly, is that you distributed the exponent over addition. This NEVER WORKS! If you don't believe me, check this out: is
$$25=5^{2}=(2+3)^{2}=2^{2}+3^{2}=4+9=13?$$
Definitely not. So this thought doesn't work. It's so common it's called the "freshman's dream". You have to write out your expression and FOIL it:
$$(x^{1/2}+x^{-1/2})^{2}=(x^{1/2}+x^{-1/2})(x^{1/2}+x^{-1/2}).$$
Now do your firsts, outers, inners, and lasts. What do you get?
 

linapril

New member
Dec 21, 2012
23
I got the right answer, thank you so much :)
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,197
You're welcome! Have a good one.