For this case we must simplify the following expression:
[tex]\sqrt {\frac {16} {25}}[/tex]
We can rewrite 16 as:[tex]2 ^ 4 = 2 * 2 * 2 * 2[/tex]
We can rewrite 25 as:[tex]5 ^ 2 = 5 * 5[/tex]
[tex]\sqrt {\frac {2 ^ 4} {5 ^ 2}} =\\\frac {\sqrt {2 ^ 4}} {\sqrt {5 ^ 2}} =[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
Then, rewriting the expression:
[tex]\frac {2 ^ 2} {5} =\\\frac {4} {5}[/tex]
Answer:
[tex]\frac {4} {5}[/tex]
