Answer:
[tex] \frac{3}{5} m^2 |n|^{3} [/tex]
1) given
[tex] \sqrt{ \frac{225}{625}m^4n^6 } [/tex]
2) factor 225 and 625
[tex]225=15^2
625=25^2
\sqrt{ \frac{15^2}{25^2}m^4n^6 } [/tex]
3) extract the factors from the radical dividing the exponents by the index of the radical
2/2 = 1 => exponent = 1 => [tex] \frac{15}{25} [/tex]
4/2 = 2 => exponent = 2 => [tex] m^{2} [/tex]
6/2 = 3 => exponent = 3=> [tex] n^{3} [/tex]
[tex] \frac{15}{25} m^2n^3[/tex]
4) simplify the fraction 15/25 = 3/5
=>
[tex] \frac{3}{5} m^2n^3[/tex]
and you add the absolute symbols | | because it can only be positive.
