If n is an odd number, then the radical expression sqrt(a^n) simplifies to a. If n is even, the expression sqrt(a^n) simplifies to |a|.
4y^6|x|
Practice makes perfect
For any real number a, the radical expression sqrt(a^n) can be simplified as follows.
sqrt(a^n)=
a if n is odd
|a| if n is evenBecause the given root has an even index and the variables have even exponents, we will use the absolute value symbol to simplify the expression.
Since y is raised to an even power, y^6 is positive. Therefore, |y^6| = y^6. Let's simplify our expression further.
4|x| * |y^6| = 4y^6|x|
This is the simplest form of the given expression.
