[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
       ____________             multiply add exponents
        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
         _________              multiply add exponents
          9a4b4  

=      -6ab                         divide subtract exponents

result:  -6ab


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

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

=        -500a5b3
      _____________      multiply add exponents
          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
     ______________          multiply add exponents
         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