Question

30 PTS!!! PLEASE HELP ME HURRY!!!!! What values complete each statement? Enter your answers in the boxes. (16−−√)2 = (empty box)   in simplest form. By the Power of Power rule, (1612)2=1622 . So, 1612 must equal (empty box) in radical form.

Answer 1

Answer: $(\sqrt{16})^2= 16$

$16^{\frac{1}{2}}$ must equal $\sqrt{16}$ in radical form.

Step-by-step explanation: Given radical expression $(\sqrt{16})^2$.

First we would convert square root by exponent form.

Square root represents power 1/2.

Therefore,

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

We know power rule $(x^a)^b= x^{a\times b}$.

Therefore,

By the Power of Power rule,

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

On simplifying powers, we get $1/2 \times 2 = 1$.

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

So, $16^{\frac{1}{2}}$ must equal $\sqrt{16}$ in radical form.