How do you simplify x−4y−6z−10(a1b2c−4)2⋅a1bc−4(x6yz9)2?

1 Answer
Pythagoras
Sep 20, 2015

c4x16⋅y8⋅z28⋅a1⋅b3

Explanation:

As always, "count apples as apples and oranges as oranges".
In this case everything are really just multiplications and divisions.
If I see this, I would just open up the parentheses and see what can be removed. The remaining terms have to be the answer.

So let's attack this.
We have:
x−4y−6z−10(a1b2c−4)2⋅a1bc−4(x6yz9)2

Then, I would rewrite b=b1 (although it is unnecessary), and y=y1 just to be explicit.
Open the parentheses. Remember the rule: (an)m=an⋅m
We get:
x−4y−6z−10a2b4c−8⋅a1b1c−4x12y2z18

Then it's easy, x goes with x, y goes with y, etc...
Remember the rule anam=an−m
So we have:
x−4−12⋅y−6−2⋅z−10−18⋅a1−2⋅b1−4⋅c−4+8
=x−16⋅y−8⋅z−28⋅a−1⋅b−3⋅c4
or rewriting it in fractional form (putting all the negative exponents at the bottom):

=c4x16⋅y8⋅z28⋅a1⋅b3

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