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 rad…

Question

asked Apr 16, 2019 230k views

2 Answers

Liberty Lover · Answer 1 · 2019-04-20T11:12:52+0000

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