Exponents

[psi20]

If you had b^(m/n), is it

a) nthroot of (b to the mth)

b) (nthroot of b) to the mth

c) either

d) both

[NSX]

All of the above.

[psi20]

Now I'm really confused! When I say both, I mean both a and b. When I saw either, I mean either a or b.

[NSX]

Okay, then d

[Dave]

Use the laws of indices:

 

[math]\(a^{b}\)^{c}=a^{bc}[/math].

 

So [math]a^{m/n}=\(a^{m}\)^{1/n}=\(a^{1/n}\)^{m}[/math]

[psi20]

Oh yeah, that makes sense.

 

But now this doesn't make sense.

If 4^(1/2) = +/- 2

Then 8^(1/3) = +/- 2 too?

8^(1/3) = (8^(2/3))^(1/2)

But if -2 is a root of 8^(1/3), then why doesn't -2^3 = 8? Or maybe -2^3 = 8?

 

Also look at this:

2^2 = 2^(4 x 1/2) = etc. etc. and that means 2^2 = +/- 4.

[NSX]

psi20 said in post # :

But now this doesn't make sense.

If 4^(1/2) = +/- 2

Then 8^(1/3) = +/- 2 too?

8^(1/3) = (8^(2/3))^(1/2)

But if -2 is a root of 8^(1/3), then why doesn't -2^3 = 8? Or maybe -2^3 = 8?

 

[math]\sqrt{4}[/math] :neq: [math]\pm2[/math]

 

psi20 said in post # :

Also look at this:

2^2 = 2^(4 x 1/2) = etc. etc. and that means 2^2 = +/- 4.

 

No it doesn't.

 

I think the problem you're encountering is that the [math]\pm[/math] only arises when you're solving for the argument being squared, cubed, etc.

 

ie. if [math]x^2 = 4[/math], then [math]x=\pm2[/math]

Likewise, [math]\sqrt{4}=2[/math] & [math]-\sqrt{4}=-2[/math]

 

--

 

i see mimeTeX doesn't like spaces.

[Dave]

This was a great source of confusion for my maths class a few years back when we were learning the basics. Say if you have [math]x^2-4=0[/math]. Then [math]x^2=4[/math]. So you want to find a value for [math]x[/math] such that when you square it, it decides to become 4.

 

However, when you draw the graph of the function, it becomes fairly clear that there's actually 2 solutions. The problem is that when you square a negative number, the answer is positive. So in this case, the answer would involve a plus/minus sign.

 

--

I noticed this a while back, all the math tags actually do is encapsulate the stuff you put in them and execute a cgi script from the looks of it. You can't really have spaces in the request you send to the webserver easily so I think mimeTeX just ignores them.

[psi20]

Ah man, the pictures don't show up. They are boxes with the red x in them, can you show me it without pictures?

 

I once got replies of the square root of 4 equalling +/- 2. So the square root of four isn't -2?

 

I get that if x^2 = 4, x = +/- 2. But I'm wondering if an expression sqroot 4 = +/- 2

[fafalone]

When you multiply two negative numbers together, you get a positive number. Hence -2 is also a solution for x² = 4.

[psi20]

Yup, I know that, but is 4^0.5 = +/-2?

[NSX]

NSX said in post # :

[math]\sqrt{4}=2[/math] & [math]-\sqrt{4}=-2[/math]

 

It's just like graphing [math]y=\sqrt{x}[/math] with a graphing calculator, or other graphing utility. In order to properly create [math]y=x^2[/math]'s inverse, you have to graph both [math]y=\sqrt{x}[/math] and [math]y=-\sqrt{x}[/math].

[fafalone]

psi20 said in post # :

Yup, I know that, but is 4^0.5 = +/-2?

 

No. That's performing a power operation on a number, not solving an equation.