1. ## Simplifying Rational Powers

Bah, okay.

I'm trying to find a common denominator right now for this part of the problem:

$\displaystyle 4/3-5/6$

Don't I multiply the denominators together? Thus making it?

$\displaystyle 24/18-15/18$

Now since I can subtract the numerators it means I get 9. $\displaystyle 9/18 = 1/2$

That ends up as the right answer for the exponent of this: $\displaystyle 12x^1/2/y^4/3$

However, in the solution it baffles me because they got the following:

$\displaystyle = (4*3)x^4/3-5/6/y^4/3$

= 12x^8/6-5/6/y^4/3

It looks like they just multiplied it by two, but I didn't think that was how you got a common denominator...

$\displaystyle = 12x^1/2/y^4/3$

2. Originally Posted by A Beautiful Mind
Bah, okay.

I'm trying to find a common denominator right now for this part of the problem:

$\displaystyle 4/3-5/6$

Don't I multiply the denominators together? Thus making it?

$\displaystyle 24/18-15/18$

Now since I can subtract the numerators it means I get 9. $\displaystyle 9/18 = 1/2$

That ends up as the right answer for the exponent of this: $\displaystyle 12x^1/2/y^4/3$

However, in the solution it baffles me because they got the following:

$\displaystyle = (4*3)x^4/3-5/6/y^4/3$

= 12x^8/6-5/6/y^4/3

It looks like they just multiplied it by two, but I didn't think that was how you got a common denominator...

$\displaystyle = 12x^1/2/y^4/3$
Think what the lowest common denominator of 3 and 6 is (it's not 18, nor 12)

3. Originally Posted by A Beautiful Mind
Bah, okay.

I'm trying to find a common denominator right now for this part of the problem:

$\displaystyle 4/3-5/6$

Don't I multiply the denominators together? Thus making it?
No. If the two denominators are relatively prime, then yes, you would multiply the denominators together. But here, one number is a multiple of another. In that case, the common denominator would simply be the bigger number.

I'm aware of two methods to finding LCD's. This site explains both: How To Find The Least Common Denominator (LCD) .

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