SOLUTION: Ok, it just looks like all the help I've seen is too advanced to help me with this... here's the problem... (a^3 b^-6)^1/2.. I know this has to be simple, but I've been wracking m

Algebra ->  Radicals -> SOLUTION: Ok, it just looks like all the help I've seen is too advanced to help me with this... here's the problem... (a^3 b^-6)^1/2.. I know this has to be simple, but I've been wracking m      Log On


   

Question 30441: Ok, it just looks like all the help I've seen is too advanced to help me with this... here's the problem... (a^3 b^-6)^1/2.. I know this has to be simple, but I've been wracking my brain trying to figure it out.
Thanks!
Charity
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
there are several ways to do this. first, ^1/2 means the same as square root. for this it would be just as easy to do the root first ... as it would be to distribte the power and then root it out. I will show you both.
Root first:
+%28a%5E3b%5E-6%29%5E%281%2F2%29+
+sqrt+%28a%5E3b%5E-6%29+ make the b power's value positive.
+sqrt+%28%28a%5E3%29%2F%28b%5E6%29%29+ break into separate roots
+%28sqrt+%28a%5E3%29%29%2F%28sqrt%28b%5E6%29%29+ root out the numerator
+a%28sqrt+%28a%29%29%2F%28sqrt%28b%5E6%29%29+ root out the denominator
+a%28sqrt+%28a%29%29%2Fb%5E3+
Now ... lets work it by distributing the ^1/2
+%28a%5E3b%5E-6%29%5E%281%2F2%29+ distribute to the a
this will give a fractional exponent
+a%5E%283%2F2%29b%5E%28-3%29+ distribute to the b and reduce the fraction
If working with fractional exponents, stop here ... if the simplified form is to be in radicals .... work the a value.
^3/2 is the same as +sqrt+%28a%5E3%29+
+a%28sqrt+%28a%29%29b%5E%28-3%29+ deal with the negative exponent on the b
+a%28sqrt+%28a%29%29%2Fb%5E3+
Both work. There are many ways to come about the same answer.