Quiz about AA C&C Quiz REVIEW - Radical Expressions & Rational Exponents

Question 1

Which exponential equation is equivalent to $$\left(\sqrt[3]{t}\right)^2$$

Accepted Answer

$$t^{\frac{2}{3}}$$

Answer

$$t^{\frac{3}{2}}$$

Answer

$$\frac{1}{t^{\frac{2}{3}}}$$

Answer

$$t^{\frac{1}{3}}$$

Question 2

Rewrite using a rational exponent

$$\left(\sqrt[]{7x}\right)^5$$

Accepted Answer

$$\left(7x\right)^{\frac{5}{2}}$$

Answer

$$7x^{\frac{1}{5}}$$

Answer

$$\left(7x\right)^{\frac{2}{5}}$$

Answer

$$7x^{\frac{2}{5}}$$

Question 3

Rewrite the radical expression using a rational exponent.

$$\frac{1}{\sqrt[]{3x}}$$

Accepted Answer

$$\left(3x\right)^{-\frac{1}{2}}$$

Answer

$$\left(3x\right)^{\frac{1}{2}}$$

Answer

$$\left(3x\right)^{\frac{-2}{1}}$$

Answer

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

Question 4

Which expressions are equivalent to $$x^{\frac{3}{7}}$$ ?

Choose ALL that apply!

Accepted Answer

$$\sqrt[7]{x^3}$$

Accepted Answer

$$\left(x^{\frac{1}{7}}\right)^3$$

Accepted Answer

$$\left(\sqrt[7]{x}\right)^3$$

Answer

$$\left(x^7\right)^{\frac{1}{3}}$$

Answer

$$\sqrt[3]{x^{\frac{1}{7}}}$$

Question 5

Which expressions are equivalent to $$z^{0.4}$$ ?

Choose ALL that apply!

Accepted Answer

$$z^{\frac{2}{5}}$$

Accepted Answer

$$\sqrt[5]{z^2}$$

Accepted Answer

$$\left(z^{-4}\right)^{\frac{-1}{10}}$$

Answer

$$\sqrt[4]{z}$$

Answer

$$\frac{1}{z^4}$$

Question 6

Rewrite the expression in the form xⁿ

$$\left(x^2\right)^{\frac{7}{3}}$$

Accepted Answer

$$x^{\frac{14}{3}}$$

Answer

$$x^{\frac{13}{3}}$$

Answer

$$x^{-\frac{1}{3}}$$

Answer

Question 7

Which expressions are equivalent to

$$\frac{x^{\frac{1}{5}}}{x}$$ ?

Choose ALL that apply!

Accepted Answer

$$x^{-\frac{4}{5}}$$

Accepted Answer

$$x^{\left(\frac{1}{5}-1\right)^{ }}$$

Answer

$$x^{\frac{1}{5}}-1$$

Answer

$$\frac{1}{5}$$

Answer

$$x^{\left(\frac{1}{5}+1\right)}$$

Question 8

Which expressions are equivalent to

$$x^{\frac{2}{5}}\cdot x^{-3}$$ ?

Choose ALL that apply!

Accepted Answer

$$x^{\left(\frac{2}{5}-3\right)^{ }}$$

Accepted Answer

$$x^{-\frac{13}{5}}$$

Answer

$$x^{\frac{17}{5}}$$

Answer

$$x^{-\frac{6}{5}}$$

Answer

$$x^{\left(\frac{2}{5}+3\right)}$$

Question 9

Simplify. Rewrite as a POSITIVE rational exponential expression

$$\left(x^{\frac{3}{4}}y\right)^5$$

Accepted Answer

$$x^{\frac{15}{4}}y^5$$

Answer

$$x^{\frac{23}{4}}y^6$$

Answer

$$x^{\frac{35}{4}}$$

Answer

$$x^{\frac{15}{4}}$$

Question 10

Which expressions are equivalent to

$$\frac{x^6}{\sqrt[]{x}}$$ ?

Choose ALL that apply!

Accepted Answer

$$x^{\left(6-\frac{1}{2}\right)}$$

Accepted Answer

$$x^{\frac{11}{2}}$$

Answer

$$x^{\left(6\cdot2\right)}$$

Answer

$$x^{\left(6\div\frac{1}{2}\right)}$$

Answer

Question 11

Which expressions are equivalent to

$$\left(x^{\frac{1}{5}}\right)^3\cdot\sqrt[5]{x^4}$$ ?

Choose ALL that apply!

Accepted Answer

$$x^{\left(\frac{3}{5}+\frac{4}{5}\right)}$$

Accepted Answer

$$x^{\frac{3}{5}}\cdot x^{\frac{4}{5}}$$

Answer

$$x\frac{7}{5}$$

Answer

$$x^{\frac{5}{7}}$$

Answer

$$x^{\frac{3}{5}}\cdot x^{\frac{5}{4}}$$

AA C&C Quiz REVIEW - Radical Expressions & Rational Exponents

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