Question 48555
<pre><font size = 5><b>Factor, using the given factor. Assume all variables 
represent positive real numbers.

2k<sup>-3</sup> + k<sup>-8</sup> ; k<sup>-8</sup> 

It means to put the k<sup>-8</sup> on the left, followed 
by an open parentheses with a couple blanks and
a + sign between like this:

k<sup>-8</sup>(    +    )    
    ŻŻŻ   ŻŻ
and then fill in those two blanks in the parentheses 
with two terms such that if you were to distribute it
out you would get the original expression 2k<sup>-3</sup> + k<sup>-8</sup>.

To find out what goes in the first blank divide 2k<sup>-3</sup> 
by k<sup>-8</sup> by subtracting exponents -3 MINUS -8.  Do that 
out to the side or on scrap paper, like this

(-3) - (-8) =  -3 + 8 = 5   

then write 2k<sup>5</sup> in the first blank

k<sup>-8</sup>(2k<sup>5</sup> +    )
    ŻŻŻ   ŻŻ
To find out what goes in the second blank divide 2k<sup>-8</sup> by
k<sup>-8</sup> by subtracting exponents -8 MINUS -8.  Do that out to 
the side or on scrap paper, like this

(-8) - (-8) =  -8 + 8 = 0 

So that means k<sup>0</sup> goes in the second blank.

k<sup>-8</sup>(2k<sup>5</sup> + k<sup>0</sup> )
    ŻŻŻ   ŻŻ

But k<sup>0</sup> is just 1, so we erase the k<sup>0</sup> and put a 1 there

k<sup>-8</sup>(2k<sup>5</sup> +  1 )
    ŻŻŻ   ŻŻ
Answer:

k<sup>-8</sup>(2k<sup>5</sup> + 1)

Edwin</pre>