# 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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Mechanical EngineerCommented:
Double-check step 1 in your simplification. You should have a minus sign on the bottom.

(3)/(-3) = -1
Mechanical EngineerCommented:
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.
Author 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
Commented:
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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Mechanical EngineerCommented:
[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
Commented:
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.
Author Commented:
That was right in front of my face and I didn't see it,  Thanks.
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Math / Science

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