Question

What values complete each statement?

Enter your answers in the boxes.

(7√)^2 = _____
in simplest form.

By the Power of a Power rule, (712)2=722 .

So, 712 must equal______
in radical form.

Answer 1

in its radical form

Step-by-step explanation:

Answer 2

For this case we have:

By properties of the radicals
`\sqrt {a} = a ^{\frac {1} {2}}`

So:

`(\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2`.

Now, for power properties we have:

`(b ^ {\frac {c} {d}}) ^ e = b ^ {\frac {c * e} {d}}`

Thus,
`(7 ^ {\frac {1} {2}}) ^ 2 = 7 ^ {\frac {2} {2}} = 7`

So:

`7 ^ {\frac {1} {2}} = \sqrt {7}`in its radical form

Answer:

`(\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2= 7 ^ {\frac {2} {2}} = 7` in its simplest form.

`7 ^ {\frac {1} {2}} = \sqrt {7}`in its radical form