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:
`(√(16))^2= 16`

`16^{(1)/(2)}` must equal
`√(16)` in radical form.

Step-by-step explanation: Given radical expression
`(√(16))^2`.

First we would convert square root by exponent form.

Square root represents power 1/2.

Therefore,

`(√(16))^2= (16^(1/2))^2`

We know power rule
`(x^a)^b= x^(a* b)`.

Therefore,

By the Power of Power rule,

`(16^(1/2))^2 = 16^(1/2 * 2)`

On simplifying powers, we get
`1/2 * 2 = 1`.

Therefore,
`16^(1/2 * 2) = 16.`.

So,
`16^{(1)/(2)}` must equal
`√(16)` in radical form.