[dividing monomials][section 34]

(1.)    x6
____                  here is the problem
x

=      x5             subtract exponents

result:  x5

(2.)     4ab2(-5ab3)
_____________                   here is the problem
10a2b2

=       -20a2b5
10a2b2

=     -2b3              divide subtract exponents

result:  -2b3

(3.)   (-3ab2)2
___________                   here is the problem
6ab

=      9a2b4
__________
6ab                 square -3, multiply exponents

=       3ab3
______     reduce and subtract exponents
2

result:    3ab3
_____
2

(4.)   (3ab2)2(-6a3b)
________________              here is the problem
(3a2b2)2

=   (9a2b4)(-6a3b)
____________________       square 3, multiply exponents
(9a4b4)

=        -54a5b5
9a4b4

=      -6ab                         divide subtract exponents

result:  -6ab

(5.)     (5ab)2(-20a3b)
_________________                 here is the problem
4a2b3

(25a2b2)(-20a3b)
_________________       square 5, multiply exponents
4a2b3

=        -500a5b3
4a2b3

=     -125a3              divide subtract exponents

result:  -125a3

(6.)    (5a2b)2(-100b3)
____________________         here is the problem
(52b)2

=     (25a4b2)(-100b3)    square 5, multiply exponents
____________________
625b2            square 5 twice, multiply exponents

=      -2500a4b5
625b2

=       -4a4b3               divide, subtract exponents

result:  -4a4b3

(7.)      a3x
______               here is the problem
a2x

=        ax           subtract exponents

result:  ax

(8.)   xu-vyw-z
_____________           here is the problem
x2v-uyw

=    x2u-3vy-z                 subtract exponents

result:  x2u-3vy-z

(9.)    ab2c4d2-k
________________             here is the problem
ac3dk

=    b2cd2-2k         subtract exponents

result:  b2cd2-2k

(10.)    (y3a-9)6
____________                 here is the problem
y2a-4

=      y18a-54
____________              multiply exponents
y2a-4

=      y16a-58       subtract exponents

result:  y16a-58