Computer game physics engines use algebra formulas and exponents to calculate movement and interactions in a game. If the mathematics in the game engine is incorrect, the game will not play as expected. Exponent rules must be followed carefully when multiplying terms with exponents, such as adding exponents when bases are the same and expanding exponents when bases are different. Examples are provided to demonstrate simplifying terms with exponents correctly.

1. Image Source: http://www.cheatcc.com

2. Computer Games use "Game Physics Engines" which
are low level programs inside the game to calculate the
movement, interactions, and the geometry involved with
the game.
These programs use lots of Algebra formulas in their
Algorithms, and many of these formulas involve multiplying
powers terms containing exponents.
If the mathematics isn't correct in
the game engine, then the game
is not going to play at all like we
would expect it to.
Image Source: http://cheezburger.com

3. The little number “4” is called the
“Index” or “Exponent” and tells us
how many times to multiply out
the big number “2”
The big number “2” is called the “base”
and is what we multiply together
4
2 = 2x2x2x2
Multiply four of the Base Number

4. 3 4
Let’s consider 2 x 2
We expand the exponents and get:
2x2x2 x 2x2x2x2
In total we now have seven multiplies of 2,
and so the simplified answer is:
3 4 3+4 7
2 x2 =2 = 2 = 128

5. 3 4
Let’s consider m x m
We expand the exponents and get:
mxmxm x mxmxmxm
In total we now have seven multiplies of m,
and so the simplified answer is:
3 4 3+4 7
m xm =m = m

6. m n
Let’s consider a x a
If we have any base that is the same “a”,
then we can skip expanding out the powers
of the exponents “m’ and “n”, and use the
fast track rule which is to Add the Exponents
m n m+n
a x a =a
This rule works for both letters and numbers

7. 3 4
Let’s consider 2 x m
We expand the exponents and get:
2x2x2 x mxmxmxm
Here we have different bases, so we cannot
combine the seven items using the fast rule !
23 x m4 = 2 x 2 x 2 x m4 = 8 x m4 = 8m4

8. WARNING: We cannot combine the Power
Terms and add their exponents if the big
number or letter Bases are different !
3 4 3+4 7
2 x m = 2m = 2m
Different Bases It is wrong to combine them like this
Images from Clker.com

9. To Multiply Exponents Terms, follow these steps:
 Expand terms using multiplication signs, but
do not expand the Exponent Powers terms
 Rearrange the order of the items so that the
numbers come first. Then after the numbers,
group all the letter terms in alphabetical order
 Work out the numbers answer, and add exponents
for like bases terms
 Remove all multiplication signs and spaces

10. 3 8
Simplify: b x b
Apply Powers Rule: am x an = am + n
= b3 x b8
3+8
= b
11
= b

11. 5
Simplify: 8a x 5a
= 8 x a5 x 5 x a1 (Group Numbers)
= 8 x 5 x a5 x a1 am x an = am + n
5+1
= 40 x a
= 40a6

12. 3 4 2
Simplify: 9a b x 2a
= 9 x a3 x b4 x 2 x a2
= 9 x 2 x a3 x a2 x b4
3+2 4
= 18 x a x b
= 18a5b4

13. 5 7 -7a2b4
Simplify: 3a b x
= 3 x a5 x b7 x -7 x a2 x b4
= 3 x -7 x a5 x a2 x b7 x b4
-21 5+2 7 +4
= x a x b
= -21a7b11

14. Simplify: -2d4k4 x -dk
= -2 x d4 x k4 x -1 x d1 x k1
= -2 x -1 x d4 x d1 x k4 x k1
4+1 4 +1
= 2 x d x k
= 2d5k5

15. http://passyworldofmathematics.com
Visit our Site for Free Mathematics PowerPoints