Quiz about Topic 5 - Rational Exponents and Radical Functions

Question 1

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

Accepted Answer

$$\left(x^3\right)^{\frac{1}{4}}$$

Accepted Answer

$$\sqrt[4]{x^3}$$

Answer

$$x^{\frac{8}{6}}$$

Answer

$$\left(x^{\frac{1}{4}}\right)^{\frac{2}{4}}$$

Answer

$$\sqrt[3]{x^4}$$

Question 2

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

Accepted Answer

3m3n

Answer

9m3n

Answer

9m6n2

Answer

3m8

Question 3

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

Accepted Answer

$$8\sqrt[3]{2}+6\sqrt[]{2}$$

Answer

$$\sqrt[3]{250}+\sqrt[3]{54}+\ \sqrt[]{72}$$

Answer

$$14\sqrt[3]{2}$$

Answer

$$5\sqrt[]{10}+3\sqrt[]{6}+6\sqrt[]{2}$$

Question 4

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

Accepted Answer

$$1-2\sqrt[]{2}$$

Answer

$$-\sqrt[]{2}$$

Answer

$$7\sqrt[]{2}$$

Answer

$$9\frac{1}{3}$$

Question 5

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)

Accepted Answer

Adding 12 to 4x translates the graph left 3 units.

Accepted Answer

Multiplying x by 4 stretches the graph vertically by a factor of 2.

Answer

Adding 12 to 4x translates the graph left 12 units

Answer

Multiplying x by 4 stretches the graph vertically by a factor of 4.

Answer

Multiplying x by 4 compresses the graph horizontally by a factor of 2.

Question 6

What radical function is represented by the graph?

Accepted Answer

$$f\left(x\right)=\sqrt[3]{x-1}+3$$

Answer

$$f\left(x\right)=\sqrt[3]{x+1}+3$$

Answer

$$f\left(x\right)=\sqrt[]{x+1}+3$$

Answer

$$f\left(x\right)=\sqrt[3]{3x}$$

Question 7

Identify the rule for $$\frac{f}{g}\ when\ f\left(x\right)=-3x-6\ and\ g\left(x\right)=x^2-x-6.$$

Accepted Answer

$$\frac{f\left(x\right)}{g\left(x\right)}=\frac{-3}{x-3}$$

Answer

$$\frac{f\left(x\right)}{g\left(x\right)}=\frac{-2}{\left(x+2\right)}$$

Answer

$$\frac{f\left(x\right)}{g\left(x\right)}=\frac{-3\left(x-2\right)}{\left(x-6\right)\left(x+1\right)}$$

Answer

$$\frac{f\left(x\right)}{g\left(x\right)}=\frac{3}{\left(x+2\right)}$$

Topic 5 - Rational Exponents and Radical Functions

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