translations with exponents help

[Guest]

please tell me where I am going wrong!!!! I have spent hours on this one problem.

(6a^5b)^2 1
------------ . ---------
8ab^-2 2a^-3b First i figure to eliminate the negative eponent by
taking the reciprocal of the quanity within the ().

36a^-10b^-2 1
--------------- . --------
16a^-2b^-4 2a^-3b take the reciprocal of the base and make the
exponent positive

16a^-2b^-4 . 1
-------------- ------- subtract the exponents
36a^-10b^-2 2a^-3b

16a^-2-(^-10) . 1
--------------- ------
36 2a^-3b

16a^8b^-2 . 1
-------------- ----------
36 2a^-3b

16a^8b^-2 . 1= 16a^8b^-2 divided by
36 . 2a^-3b= 72a^-3b

16a^5b^-2
------------ The answer in the book says it should be 8a^15
72 -------
9b^7

surely someone can shine some light on what the heck I am doing wrong.
I appreciate it so much! :roll:
72

 

[tkhunny]

please tell me where I am going wrong!!!! I have spent hours on this one problem.

(6a^5b)^2 1
------------ . ---------
8ab^-2 2a^-3b First i figure to eliminate the negative eponent by
taking the reciprocal of the quanity within the ().

36a^-10b^-2 1
--------------- . --------
16a^-2b^-4 2a^-3b take the reciprocal of the base and make the
exponent positive

I do not understand this. You keep SAYING it, but not actually DOING it.

1/a^-3

Say it again.
"take the reciprocal of the base and make the exponent positive"

Now, actually do it:

1/a^-3 = a³

From here:
<PRE>
(6a^5b)^2 1
------------ . ---------
8ab^-2 2a^-3b First i figure to eliminate the negative eponent by
taking the reciprocal of the quanity within the ().
</PRE>
Get
<PRE>
(6a^5b)^2*b^2 a^3
---------------- . ---------
8a 2b
</PRE>