Answer: option a.
Step-by-step explanation:
Given the expression [tex]\sqrt{8^{17}}[/tex], you need to remember:
The Product of powers property:
[tex]a^m*a^n=a^{(m+n)}[/tex]
The Power of a power property:
[tex](a^m)^n=a^{mn}[/tex]
And:
[tex]\sqrt[n]{a^n}=a[/tex]
Therefore, as the index of the radical is 2, you can rewrite [tex]8^{17}[/tex] as:
[tex]8^{17}=8^{16}*8[/tex]
Rewrite this and simplify. Then:
[tex]=\sqrt{8^{17}}[/tex]
[tex]=\sqrt{8^{16}*8}=\sqrt{8^{16}}\sqrt{8}=\sqrt{(8^{8})^2}\sqrt{8}=8^8\sqrt{8}[/tex]
This matches with the option a.
