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

E

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

Answer 2

Answer: E) x^5

`\sqrt{x^(10)} = x^5`

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Step-by-step explanation:

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

So the rule is
`√(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.