exponents

[mouchete_blanc_boxeur]

I know how to simplify different bases that stand on opposite sides of the fraction bar, but what about this...

u^-4 v^6
-------------------
v^-14 u^3 v^17

How would you group the terms with the same bases when there are three of one and two of the other?

 

[royhaas]

You only have two bases, u and v. A fraction bar just means you subtract exponents on the bottom from those on the top. On the "same side", you still add exponents of the same base.

 

[Mrspi]

I know how to simplify different bases that stand on opposite sides of the fraction bar, but what about this...

u^-4 v^6
-------------------
v^-14 u^3 v^17

How would you group the terms with the same bases when there are three of one and two of the other?

Did you notice that there are TWO factors with "v" as a base in the denominator? Let's rearrange the factors in the denominator:

xxxu<SUP>-4</SUP> v<SUP>6</SUP>
---------------
u<SUP>3</SUP> v<SUP>-14</SUP> v<SUP>17</SUP>

You can multiply those two factors with "v" as base. Remember that when you multiply powers of the same base, you add the exponents. So, v<SUP>-14</SUP> * v<SUP>17</SUP> is v<SUP>(-14) + 17</SUP>, or v<SUP>3</SUP>. Now, your fraction looks like this:

u<SUP>-4</SUP>*v<SUP>6</SUP>
-------------
u<SUP>3</SUP>*v<SUP>3</SUP>

You've indicated that you know what to do at this point, so I'll let you finish it.

I hope this helps you.