Question

How do you simplify `sqrt(x^10y^8z^2)`?

Answer 1

See the entire solution process below:

Explanation:

First, we can rewrite this expression using this rule for exponents and radicals:

`root(color(red)(n))(x) = x^(1/color(red)(n))`

`sqrt(x^10y^8z^2) = root(color(red)(2))(x^10y^8z^2) = (x^10y^8z^2)^color(red)(1/2)`

We can now use these two rules of exponents to complete the simplification:

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

`(x^color(red)(10)y^color(red)(8)z^color(red)(2))^color(blue)(1/2) = x^(color(red)(10) xx color(blue)(1/2))y^(color(red)(8) xx color(blue)(1/2))z^(color(red)(2) xx color(blue)(1/2)) = x^5y^4z^1 = x^5y^4z`