Question 40957
<pre><font size = 5><b>Multiply 

         -3a<sup>2</sup>b      14a<sup>3</sup>b<sup>2</sup>
        ———————— × ————————
          35a<sup>5</sup>      -9b<sup>4</sup>

The long way but sure way:

Write a<sup>2</sup> as aa
Write 14 as 2·7
Write a<sup>3</sup> as aaa
Write b<sup>2</sup> as bb
Write 35 as 5·7
Write a<sup>5</sup> as aaaaa
Write 9 as 3·3
Write b<sup>4</sup> as bbbb

        -3aab      2·7aaabb
      —————————— × —————————
       5·7aaaaa    -3·3bbbb

Indicate the multiplication of numerators and 
denominators

        -3aab·2·7aaabb
      ————————————————————
       5·7aaaaa(-3)·3bbbb

Cancel the -3's

        <s>-3</s>aab·2·7aaabb
      ————————————————————
       5·7aaaaa<s>(-3)</s>·3bbbb  

            aab·2·7aaabb
          ————————————————
           5·7aaaaa·3bbbb
                     
Cancel the 7's

            aab·2·<s>7</s>aaabb
         ———————————————
            5·<s>7</s>aaaaa·3bbbb

            aab·2aaabb
           ————————————
            5aaaaa·3bbbb

Cancel the 5 a's in the top into the 5 a's 
in the bottom:

            <s>aa</s>b·2<s>aaa</s>bb
           ————————————
            5<s>aaaaa</s>·3bbbb

             b·2bb
           ————————
             5·3bbbb

Cancel the three b's in the top into three of 
the b's in the bottom


             <s>b</s>·2<s>bb</s>
           ————————
             5·3<s>bbb</s>b

                   2
                ——————
                 5·3b

Write 5·3 as 15

                   2
                 —————
                  15b

Edwin
AnlytcPhil@aol.com</pre>