simplify ((8a^2)/(b^9))^-1

Question

simplify the expression: ((8a²)/(b⁹))^-1

Answer 1

Hi Jacob -- (Num/Denom)^ -1 means invert to (D/N) ... (N/D)^ -2 "flips to" D^2/(N^2), etc :)

Answer 2

So you have,

 

(8a² / b⁹)^-1                          (see shortcut at end...)

 

there are a couple of ways to attack this.  you can first multiply each power inside the parenthesis by -1 and then deal with the negative power or deal with the negative power right away.  Let's try the former...

 

multiply each power by -1.  why?  When you raise a power to a power, you keep the base and multiply the powers.

 

so you get, 8a^-2 / b^-9

 

then to get rid of a negative power you simply swap it from above the fraction to below and visa versa, and change the sign of the power.  (ex.  x² is also 1/x^-2, they look different but are the same)

 

if you break it up like this it may be easier to see (or not, lol):

8a^-2 _* 1

 1       b^-9

 

swap each piece to get:

 1   _*  b⁹   

 8a²   1

 

which is the same as

 b⁹      or   b⁹/8a²

8a²

 

shortcut to this one - just flip the whole fraction and  you're done!

 

your answer is b⁹/8a²

 

Answer 3

I'm not sure what happened to the answer I posted the first time but here it is again.

 

 

The negative 1 exponent indicates that the fraction should be inverted:

 

  ((8 a^2)/(b^9))^-1 becomes 1/(8 a^2/b^9) = b^9/8 a^2