For this case we must find an expression equivalent to the following:
[tex]5 \sqrt {13 ^ 3}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
In addition, we know that:
[tex]13 ^ 3 = 13 ^ 2 * 13[/tex]
Rewriting the given expression we have:
[tex]5 \sqrt {13 ^ 3} = 5 \sqrt {13 ^ 2 * 13} = 13 * 5 \sqrt {13} = 65 \sqrt {13}[/tex]
Answer:
[tex]65 \sqrt {13}[/tex]
