Math Question

[Draphoelix]

Can someone explain to me why (a^(-2)/b^5)^(-3) = (a^6)(b^15)

This is how far I got:

(a^(-2)/b^5)^(-3) = (b^5/(a^(-2))^3 = b^15/a^(-6) = ? What next ?

 

[Whitesock]

Since a^(-2) is the same as 1/a^2 you put it on the bottom, then you multiply each exponent by negative 3. This puts them both back on top.

 

[phyrex1an]

You made an error in both your first and second transition (ironically, these errors cancel each other ).

(a^(-2)/b^5)^(-3) != (b^5/(a^(-2))^3 (counterexample: a=1, b=2)
You probably mean (a^(-2)/b^5)^(-3) = (1/((a^(-2)/b^5)))^3 = 1/((a^(-2)/b^5))^3

(b^5/(a^(-2))^3 != b^15/a^(-6) (counterexample yet again: a=1, b=2). You did the same error as last time.
The law you should be using is this: http://en.wikipedia.org/wiki/Power_(mathematics)#Negative_integer_exponents

Post here again if you're unable to solve it yourself. (assuming this is homework...)

 

[Draphoelix]

Oww, I'm not so used at reading equations through the computer format.

Just to simplify things (my use of paranthes may be wrong)

If
1/a^2 = a^(-2)
is
1/a^(-2) = a^2 ?

___

And is b^15/a^(-6) = (a^6)(b^15)?

___

And isn't 1/((a^(-2)/b^5))^3 the same as (b^5/a^(-2))^3 ?

 

[phyrex1an]

If
1/a^2 = a^(-2)
is
1/a^(-2) = a^2 ?

Yes. 1/a^(-2) = 1/(1/a^2) = a^2

And is b^15/a^(-6) = (a^6)(b^15)?

Yes. b^15/a^(-6) = b^15/(1/a^6) = (a^6)(b^15)

And isn't 1/((a^(-2)/b^5))^3 the same as (b^5/a^(-2))^3 ?

Yes it is. But this isn't what you wrote in your first post
I guess your error was due to a parentheses mismatch and not mathematical error ^^ I assumed you meant (b^5)/(a^(-2))^3 when you wrote (b^5/(a^(-2))^3.

 

[Draphoelix]

Ah Sry. But thanks :thup:.

 

[Kings]

Well...I'm glad I was here to help.