# Monomial Rules

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```					Polynomials – Day 4                                                                     Name ________________________
Notes                                                                                   Date _____________ Period ______
Monomial Rule

Quotient of Powers

a5 aaaaa 2
=     =a
Examples: 3   aaa
a

xm    m -n
Rule: n = x
x
*bases must be the same to use the Quotient of Powers rule

(You can write each problem in extended form. Then divide out each form of 1 (anything over itself).
Rewrite using exponents again.)
Simplify.
x6                                x5 y2                            ( x)3 y5
1.                                2.                                3.
x3                                 x3 y2                                xy
1 1 1                                                  1 1 1             1 1                                         1 1
3                                                                  2                                                               2   4
x .x .x .x .x .x = x                                 - x . x . x . x . x . y. . y = - x                 -x . -x . -x . y . y . y. . y . y = -      x y
x .x .x                                               x .x .x .          y .y                                       x .y
(The negative stays in the front.                  (After you divide out, you must multiply the
There is nothing to multiply it with)              negative signs. Negative times a negative is a
positive. Then multiply times the third negative
which causes it to be a negative.

16x2                                                      88x5 y 4                                      x
4.                                                    5.                                                 6.
8x                                                        22x2 y3                                     x5
1 1                                           1 . . . . .1 1 1 1 1. .            3                                   1
2 .8 . x . x = 2x                               22 4 x x x x . x . y . y y y = - 4x y                                      x                  =1
4
8 .x                                          - 22                          x .x .y .y .y                          x .x .x .x .x              x
Reduce the number                                     (The negative stays in the front.)                 (When everything is divided out, a 1 is left)

 x 7 y8                                        3x10 y11                                               x3y6
7.                                                    8.                                                 9.
x2 y                                            x10 y                                                 x5 y
If bases are same, you can use the Quotient of Powers rule. It is best to use it only if the exponents on the top are the biggest.
7 -2        8–1            5       7                     10       11 – 1          10                                                          5
-x            y         = - x        y                3x            y            = 3y                    x . x . x . y . y . . y . y . y. . y = y
10                                                                                  2
x                                                  x . x . x . x . x. . y              x
1                                                  1 1 1              1

18x5 y 6                                                  2x8 y8                           ( 3x3 )2
10.                                                   11.                                      12.
3y5                                                      x5 y 5                             x 4 y2
5       6–5          5                                   8-5           8–5         3 3         2     3 2               6-4          2
6x y                = 6x y                            -2x                y         = -2x y     (-3) (x )          = 9x             = 9x
2                2
y               y
Solve.
13.    The area of a rectangle is (64x4y10). If the length of the rectangle is (2xy3), find the width.
4    10              4 - 1 10 – 3           3        7
64 x y              = 32 x           y        = 32x        y
3
2x y
Polynomials – Day 4                                              Name ________________________
Notes                                                            Date _____________ Period ______
14.           Chris has \$16x10 y12 worth of trading cards in his collection. If each card is worth 2x6 y6 , how
many cards does Chris have in his collection?
10         12          10 - 6 12 – 6          4       12
16 x          y        = 8x          y        = 8x y
6       6
2x y

15.           Audrey studied 16x18y6 hours last week. If she studied 8x3y3 days, for the same number of
hours each day, how many hours did Audrey study each day?
18         6       18 - 3 6 – 3           15          3
16 x          y = 2x                y     = 2x           y
3       3
8x y

16.           The area of a rectangle is 63x5y9. Find the width of the rectangle if its length is 9x4y6.
5       9       5-4 9–6                3
63 x y = 7x                     y        = 7xy
4       6
9x y

17.           The volume of a rectangular prism is (36x5y9). Find the length of the prism if its width is (3x2y)
and its height is (4xy3).
5 9             4-1 9–1                3       8        3-1 8-3       2    5
36 x y = 12 x                    y       = 12x y = 3x               y       = 3x y
2                                              3
3x y                                       4xy

```
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