# Simplifying Rational Powers

• Jul 13th 2009, 01:14 PM
A Beautiful Mind
Simplifying Rational Powers
Bah, okay. (Doh)

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\$
• Jul 13th 2009, 01:15 PM
e^(i*pi)
Quote:

Originally Posted by A Beautiful Mind
Bah, okay. (Doh)

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)
• Jul 13th 2009, 02:14 PM
yeongil
Quote:

Originally Posted by A Beautiful Mind
Bah, okay. (Doh)

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) .

01