Question

What is `(x^2y)^(1/2)`?

Answer 1

See a solution process below:

Explanation:

We can use these rules of exponents to simplify the expression:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))` and `a^color(red)(1) = a`

`(x^2y)^(1/2) => (x^color(red)(2)y^color(red)(1))^color(blue)(1/2) => x^(color(red)(2) xx color(blue)(1/2))y^(color(red)(1) xx color(blue)(1/2)) => x^color(red)(1)y^(1/2) => xy^(1/2)`

Or, if you want to write this in radical form:

`(x^2y)^(1/2) => sqrt(x^2y) => sqrt(x^2)sqrt(y) => xsqrt(y)`