Question

PLEASE HELP!!!!! What values complete each statement? Enter your answers in the boxes. (16‾‾‾√)2 = _ in simplest form. By the Power of Power rule, (1612)2=1622 . So, 1612 must equal _ in radical form.

Answer 1

We are given expression: $(\sqrt{16})^2$.

Square root in exponent form is power $\frac{1}{2}$.

Therefore, $\sqrt{16} = 16^{1/2}$.

Now, replacing square root of 16 by $16^{1/2}$ in original expression we are given, we get

$(\sqrt{16})^2 = (16^{1/2})^2 = (16)^2/2 = 16$.

Therefore,

$(\sqrt{16})^2$= 16 in simplest form. By the Power of Power rule, $(16^{1/2})^2=16^{2/2}$ . So, $16^{1/2}$ must equal$\sqrt{16}$ in radical form.