simplify the expression. assume all variables are positive.
third root x/y^2
x^(1/3)/y^(2/3)
This assumes you want the third (cube) root of (x/y^2).
To simplify the expression "third root (x/y^2)," we can express it using exponentiation. The third root of a number can also be written as raising that number to the power of 1/3.
So, we have:
(x/y^2)^(1/3)
To simplify further, we can distribute the exponent of 1/3 to both the numerator (x) and the denominator (y^2). This means we'll take the cube root of x and the cube root of y^2 separately.
∛x / ∛(y^2)
The cube root of x is expressed as ∛x, and the cube root of y^2 is expressed as ∛(y^2). Since y^2 is the square of y, the cube root of y^2 can also be written as y^(2/3).
So, the simplified expression is:
∛x / y^(2/3)
That's the simplified form of the expression "third root (x/y^2)."