Question 814009
<pre>

{{{8m^4sqrt(100m^9p^4)}}}

The index of a square root is 2, and write 100 as 10<sup>2</sup>: 

{{{8m^4}}}{{{""*""}}}{{{root(2,10^2m^9p^4)}}}

10 and p already has exponents that can
be divided evenly by index 2.  But m doesn't. We write
m<sup>9</sup> as m<sup>8</sup>m<sup>1</sup> so that m<sup>8</sup> will have as large as possible an exponent divisible by 2.

{{{8m^4}}}{{{""*""}}}{{{root(2,10^2m^8m^1p^4)}}}

We take 10<sup>2</sup> out of the square root as
10 with exponent 1 by dividing the index
into the exponent 2 of 10.

We take m<sup>8</sup> out of the square root as
m with exponent 4 by dividing the index
2 into the exponent 8 of x.

We take p<sup>4</sup> out of the square root as
p with exponent 2 by dividing the index 2
into the exponent 4 of p.
 And we have

{{{8m^4*10^1m^4p^2}}}{{{""*""}}}{{{root(2,m^1)}}}

{{{8m^8*10p^2}}}{{{""*""}}}{{{root(2,m)}}}

{{{80m^8p^2}}}{{{sqrt(m)}}}

Edwin</pre>