Question

If (x)²√³ = (x√x)², where x * 0, then the value of x is

Answer 1

We can simplify both sides of the equation using the rules of exponents:

(x)²√³ = (x^(2/3))^2 = x^(4/3)

(x√x)² = (x^(3/2))^2 = x^3

Now we can set the two expressions equal to each other and solve for x:

x^(4/3) = x^3

Divide both sides by x^(4/3):

x^3 / x^(4/3) = x^(9/3 - 4/3) = x^5/3 = 1

Taking the cube root of both sides:

x = 1^(3/5) = 1

Therefore, the value of x is 1.