Topic 5 - Rational Exponents and Radical Functions

Select all expressions that are equivalent to $$x^{\frac{3}{4}}$$

Simplify the expression $$\sqrt[4]{81m^{12}n^4}$$ . Assume all variables are positive.

Solve the equation -4x³ = 32.

x = ____

What is the reduced radical form of $$\sqrt[3]{250}+\sqrt[3]{54}+\sqrt[]{72}$$ ?

$$Multiply\ \left(2\sqrt[]{x}+3\right)\left(2\sqrt[]{x}-3\right).$$

$$What\ is\ \frac{7-\sqrt[]{98}}{3-\sqrt[]{2}}\ in\ reduced\ radical\ form?$$

Select all the statements that describe the relationship between the graph of $$k\left(x\right)=\sqrt[]{4x+12}-1$$ and the graph of the parent function f(x) = $$\sqrt[]{x}$$ . (Tricky question)

What radical function is represented by the graph?

The length of one side, s, of a shipping box is $$s\left(x\right)=\sqrt[3]{2x}$$ , where x is the volume of the box in cubic inches. A manufacturer needs the volume of the box to be between 108 in.³ and 256 in.³. What are the minimum and maximum possible lengths of s?

minimum: ​ (a)   in.
maximum: ​ (b)   in.

Solve the equation $$x+3=\ \sqrt[]{x+33}.$$