Question

Which expression is equivalent to ?
xy^2/9?

Answer 1

Answer:
`x\sqrt[9]{y^(2) }`

Step-by-step explanation: For all expressions in the form
`x^{(a)/(b)` , the expression is equal to
`\sqrt[b]{x^a}`. The denominator in a fractional exponent is the type of root it is. For example,
`x^(1)/(3)` is going to be the cubed root, or the

3rd root of x (
`\sqrt[3]{x}`). The numerator is what power x is raised to. For example,
`x^(3)/(2)` is going to be
`√(x^3)`.

In fractional exponents, the square root only takes the form of the variable it is assigned to. What does that mean? Well, for
`xy^(2)/(9)`, the square root only applies to the y. The x is considered a constant and can be moved out. Thus, we get
`x\sqrt[9]{y^2}`.