Not The Root

$\sqrt{16^4}$ can be expressed as :

• $\sqrt{16^4} = 16^\frac{4}{2} = 16^2$

• $\sqrt{4^{2 \times 4}} = 4^\frac{8}{2} = 4^4$

• $\sqrt{2^{4 \times 4}} = 2^\frac{16}{2} = 2^8$

Now, the only remaining option is $8^2$

$\therefore \sqrt{16^4} \neq 8^2$

First , show that $\sqrt{16^4}$ is equal to $16^2$ . This has been shown in other solutions, so look down. Or you can take my word for it. If a number is $16^2$ , then how can it also be $8^2$ . $16$ is not equal to $8$ so it is impossible for $\sqrt{16^4}$ to be both $16^2$ and $8^2$ . And since $\sqrt{16^4}$ is equal to $16^2$ . The answer to the problem is $8^2$ .