For this case we must find the value of the following expression:
[tex]\sqrt {8 ^ {17}}[/tex]
We have to:
[tex]8 ^ {17} = 8 ^ 1 * 8 ^ {16}[/tex]
Substituting:
[tex]\sqrt {8 * 8 ^ {16}}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]8 ^ {\frac {16} {2}} * \sqrt {8}\\8 ^ 8 * \sqrt {8}[/tex]
So we have to:
[tex]\sqrt {8 ^ {17}} = 8 ^ 8 * \sqrt {8}[/tex]
Answer:
[tex]8 ^ 8 * \sqrt {8}[/tex]
Option A
