Question

Which is equivalent to sqrt x^10
A. X-5
B. X -1/5
C. X sqrt 10
D. X 1/5
E. X^5

Answer 1

Answer:  E) x^5

$\sqrt{x^{10}} = x^5$

=====================================================

Explanation:

We simply take half of the exponent 10 to get 5. This applies to square roots only.

So the rule is $\sqrt{a^b} = a^{b/2}$

A more general rule is

$\sqrt[n]{a^b} = a^{b/n}$

If n = 2, then we're dealing with square roots like with this problem. In this case, a = x and b = 10.

Answer 2

Answer:

E

$\sqrt{ {x}^{10} } \\ = \sqrt{ ({x}^{5} ) {}^{2} } \\ = {x}^{5}$