Question

Which expression is equivalent to

Answer 1

Answer:

$\frac{3}{5} m^2 |n|^{3}$


1) given

$\sqrt{ \frac{225}{625}m^4n^6 }$

2) factor 225 and 625

$225=15^2 625=25^2 \sqrt{ \frac{15^2}{25^2}m^4n^6 }$

3) extract the factors from the radical dividing the exponents by the index of the radical

2/2 = 1 => exponent = 1 =>      $\frac{15}{25}$

4/2 = 2 => exponent = 2 =>      $m^{2}$ 

6/2 = 3 => exponent = 3=>       $n^{3}$


$\frac{15}{25} m^2n^3$

4) simplify the fraction 15/25 = 3/5

=>

$\frac{3}{5} m^2n^3$

and  you add the absolute symbols | | because it can only be positive.