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Equation not balancing

I have the following expression: (3a^-2 * b)/(-3a^2).  To my understanding this expression can be simplified to (-a^-4 * b) because:
3/3 = 1
a^-2/a^2 = a^-4
b remains the same
When I substitute actual values for the variables the equation doesn't balance.
a=2, b=4
-(3a^-2 * b)/(-3a^2) = -a^-4 * b
-(3(0.25)(4))/(-3(4)) = (0.0625)(4)
-3/-12 = 0.25
-0.25 = 0.25
Why is there a polarity difference?  What am I not understanding?
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NevSoFly
Asked:
NevSoFly
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1 Solution
 
byundtCommented:
Double-check step 1 in your simplification. You should have a minus sign on the bottom.

(3)/(-3) = -1
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byundtCommented:
And when you plugged values into the original equation, you put a minus sign in two places on the left side, where the original expression only had 1.
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NevSoFlyAuthor Commented:
I'm sorry both of those were typos.  The steps should be as below.  The equation still doesn't balance.

•(3a^-2 * b)/(-3a^2) = -a^-4 * b


•(3(0.25)(4))/(-3(4)) = (0.0625)(4)


•3/-12 = 0.25


•-0.25 = 0.25
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Thibault St john Cholmondeley-ffeatherstonehaugh the 2ndCommented:
You have a minus sign on the right hand side at -a^-4*b but you lose it when you get to (0.0625)(4).
The minus value should still be there.
The negative you might think you are losing is the index, not the value. The negative index just means 1/(value with positive index)
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byundtCommented:
[3a^-2*b]/(-3a^2) = -a^-4*b

Plug in a = 2 and b = 4
[3*4/(2^2)] / (-3 * 2^2) = -4/(2^4)

[3*4/4] / (-3*4) = -4/16

[3]/(-12) = -.25

-.25 = -.25
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Thibault St john Cholmondeley-ffeatherstonehaugh the 2ndCommented:
An example in case it helps:
You have -3a^2 which comes out to -3*2^2 = -12, but on your right hand side you have
-a^-4 which could be written as -1a^-4 = -1*0.0625 = -0.0625.
Hope this helps.
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NevSoFlyAuthor Commented:
That was right in front of my face and I didn't see it,  Thanks.
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