# Equations with fractional exponents.

• Jan 25th 2010, 02:02 PM
Turtle13
Equations with fractional exponents.
I have to solve a few equations that are similar to radial equations. I know how fractional exponents relate to square roots but I have something majorly wrong in my operations. I can't solve any of these. Here's one I could use help with. If I see enough steps I can easily apply it to the rest.

$\displaystyle 5x^5/3 +160=0$

It's supposed to read 5x to the 5/3rd power.

I have a test tomorrow and I'm trying to get a grip on some of this stuff that I'm not understanding. Oddly enough I can handle quadratics with fractional exponents already, I just can't do this simpler version.
• Jan 25th 2010, 02:16 PM
Jhevon
Quote:

Originally Posted by Turtle13
I have to solve a few equations that are similar to radial equations. I know how fractional exponents relate to square roots but I have something majorly wrong in my operations. I can't solve any of these. Here's one I could use help with. If I see enough steps I can easily apply it to the rest.

$\displaystyle 5x^5/3 +160=0$

It's supposed to read 5x to the 5/3rd power.

I have a test tomorrow and I'm trying to get a grip on some of this stuff that I'm not understanding. Oddly enough I can handle quadratics with fractional exponents already, I just can't do this simpler version.

you mean $\displaystyle 5x^{5/3} + 160 = 0$ ?

Note that this means $\displaystyle x^{5/3} = -32$

raise both sides to the 3/5 power (do you see why?) you get

$\displaystyle x = (-32)^{3/5}$

which i think you can finish off
• Jan 25th 2010, 03:08 PM
Turtle13
Yes, that helps immensely. I was able to solve them all with no problems.

BTW, how do I properly type that fractional exponent with the math brackets?
• Jan 26th 2010, 12:21 PM
Jhevon
Quote:

Originally Posted by Turtle13
Yes, that helps immensely. I was able to solve them all with no problems.

BTW, how do I properly type that fractional exponent with the math brackets?

if an argument or power has more than one elements in it, you must include it is {} brackets.

$$x^2/3$$ gives $\displaystyle x^2/3$

while

$$x^{2/3}$$ gives $\displaystyle x^{2/3}$
• Jan 26th 2010, 12:37 PM
masters
Quote:

Originally Posted by Jhevon
if an argument or power has more than one elements in it, you must include it is {} brackets.

$$x^2/3$$ gives $\displaystyle x^2/3$

while

$$x^{2/3}$$ gives $\displaystyle x^{2/3}$

Or....

$$x^{\tfrac{2}{3}}$$ gives you $\displaystyle x^{\tfrac{2}{3}}$, but I kinda like yours better. It's easier to read.
• Jan 26th 2010, 12:42 PM
Jhevon
Quote:

Originally Posted by masters
Or....

$$x^{\frac{2}{3}}$$ gives you $\displaystyle x^{\frac{2}{3}}$, but I kinda like yours better. It's easier to read.

indeed, i usually use \frac in a power only if the base is huge, like $\displaystyle \left( \frac {x^3 + 4x + 1}{2x + 3} \right)^{\frac 23}$

in that case, the power might look too small, so you can use \tfrac: $\displaystyle \left( \frac {x^3 + 4x + 1}{2x + 3} \right)^{\tfrac 23}$
• Jan 26th 2010, 01:03 PM
masters
Quote:

Originally Posted by Jhevon

in that case, the power might look too small, so you can use \tfrac:

Yeah, \tfrac looks better.

\frac: $\displaystyle x^{\frac{2}{3}}$

\tfrac: $\displaystyle x^{\tfrac{2}{3}}$