Question

Please help me on this

Answer 1

Answer: option a.

Step-by-step explanation:

Given the expression $\sqrt{8^{17}}$, you need to remember:

The Product of powers property:

$a^m*a^n=a^{(m+n)}$

The Power of a power property:

$(a^m)^n=a^{mn}$

And:

$\sqrt[n]{a^n}=a$

Therefore, as the index of the radical is 2, you can rewrite $8^{17}$ as:

$8^{17}=8^{16}*8$

Rewrite this and simplify. Then:

 $=\sqrt{8^{17}}$

$=\sqrt{8^{16}*8}=\sqrt{8^{16}}\sqrt{8}=\sqrt{(8^{8})^2}\sqrt{8}=8^8\sqrt{8}$

 

This matches with the option a.