Question 64750
<pre><font size = 5><b>
Simplify each expression. Use only positive exponents.
(2x^-5 y^4)^3

(2x<sup>-5</sup>y<sup>4</sup>)<sup>3</sup>

Make sure every factor, including the 2, inside the 
parentheses shows an exponent.  So give the 2 its
understood exponent of 1.

(2<sup>1</sup>x<sup>-5</sup>y<sup>4</sup>)<sup>3</sup>

Now, remove the parentheses by multiply each of the 
three inside exponents by the outside exponent 3

2<sup>1·3</sup>x<sup>-5·3</sup>y<sup>4·3</sup>

2<sup>3</sup>x<sup>-15</sup>y<sup>12</sup>

Now put this over 1

 2<sup>3</sup>x<sup>-15</sup>y<sup>12</sup>
-----------
   1

and use the rule. 

To change the sign of the
exponent of a factor of the numerator, move
the base and the exponent from numerator to
denominator, and change the sign of the
exponent only:

and vice-versa:

[To change the sign of the
exponent of a factor of the denominator, move
the base and the exponent from denominator to
numerator, and change the sign of the
exponent only]

But you need only the first rule to bove the
x<sup>-15</sup> to the bottom as x<sup>15</sup>

 2<sup>3</sup>y<sup>12</sup>
------
  x<sup>15</sup>

Now you can replace the 2<sup>5</sup> by 8, since
2·2·2 = 8

 8y<sup>12</sup>
------
  x<sup>15</sup>

Edwin</pre>