Question 24860
<pre><font size = 4><b> a<sup>3/2</sup>b<sup>3</sup>c<sup>5</sup>
—————————
  a<sup>2</sup>b<sup>1/3</sup>

 a<sup>3/2</sup>b<sup>3</sup>c<sup>5</sup>
——————————
  a<sup>2</sup>b<sup>1/3</sup>

To divide exponentials with like bases and positive exponents,
subtract their exponents, larger minus smaller, placing the
common base with the difference exponent in the numerator or
denominator, depending on which the larger exponent is in.

a<sup>2</sup> has a larger exponent than a<sup>3/2</sup> so we subtract exponents
2 - 3/2 = 4/2 - 3/2 = 1/2 and since a<sup>2</sup> has the larger 
exponent and is in the denominator, we place a<sup>1/2</sup> in the
denominator and eliminate the a<sup>3/2</sup> and the a<sup>2</sup>:

   b<sup>3</sup>c<sup>5</sup>
——————————
 a<sup>1/2</sup>b<sup>1/3</sup>
 
b<sup>3</sup> has a larger exponent than b<sup>1/3</sup> so we subtract exponents
3 - 1/3 = 9/3 - 1/3 = 8/3 and since b<sup>3</sup> has the larger 
exponent and is in the numerator, we place b<sup>8/3</sup> in the
numerator and eliminate the b<sup>3</sup> and the b<sup>1/3</sup>:

   b<sup>8/3</sup>c<sup>5</sup>
——————————
    a<sup>1/2</sup>

Edwin
AnlytcPhil@aol.com</pre></font></b>