## Roots of exponential expressions

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Sleepy Ash
Posts: 13
Joined: Mon Dec 15, 2014 1:25 am
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### Roots of exponential expressions

I would like to have a bit more specific details on what makes a problem like this

\sqrt{b^1^8}=\left| b^9 \right|

End up with an absolute value. I am having trouble comprehending what determines the answer to be in a form of an absolute value.

anonmeans
Posts: 84
Joined: Sat Jan 24, 2009 7:18 pm
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### Re: Roots of exponential expressions

...what makes a problem like this

\sqrt{b^1^8}=\left| b^9 \right|

End up with an absolute value.
I don't understand how they got that 1^8 = 9?? (b^1)^8 = (b)^8 = b^8, not b^9.

Sleepy Ash
Posts: 13
Joined: Mon Dec 15, 2014 1:25 am
Contact:

### Re: Roots of exponential expressions

...what makes a problem like this

\sqrt{b^1^8}=\left| b^9 \right|

End up with an absolute value.
I don't understand how they got that 1^8 = 9?? (b^1)^8 = (b)^8 = b^8, not b^9.
http://www.forkosh.com/mathtex.cgi?form ... 5Cright%7C Problem is suppose to look like this, but I guess I messed up on the coding.

Posts: 136
Joined: Sun Feb 22, 2009 11:12 pm

### Re: Roots of exponential expressions

I would like to have a bit more specific details on what makes a problem like this

\sqrt{b^1^8}=\left| b^9 \right|
From your second post it looks like you mean this:

$\sqrt{b^{18}\,}\, =\, \left|\, b^9\, \right|$
End up with an absolute value. I am having trouble comprehending what determines the answer to be in a form of an absolute value.
Whatever b is (+ or -) b^(18) will be positive (or 0 if b = 0). But b^9 will be negative if b is negative. So they can't be equal unless they come up with the same answers. The sqrt will always give a positive; the 9th power won't. So you have to put the positive-only back in by doing the bars.