Exponents — Advanced Math

Questions in this quiz (6)

1. Simplify this expression: $$\frac{x^{\frac{5}{6}}}{x^{\frac{1}{3}}}$$

   • $$x^{\frac{1}{2}}$$
   • $$x^{\frac{7}{6}}$$
   • $$x^{\frac{5}{3}}$$
   • $$x^{\frac{5}{2}}$$

2. Simplify this expression: $$(\sqrt[4]{x^{3}})(\sqrt[5]{x^{10}})$$

   • $$x^{\frac{5}{4}}$$
   • $$x^{\frac{4}{5}}$$
   • $$x^{\frac{11}{4}}$$
   • $$x^{\frac{1}{2}}$$

3. If $$a^{-3}b^{\frac{1}{2}}=\frac{5}{4},$$ what is the value of $$\frac{b}{a^{6}}?$$

   • $$\frac{1}{2}$$
   • $$\frac{5}{16}$$
   • $$\frac{16}{5}$$
   • $$\frac{25}{16}$$

4. For what value of $$k$$ is the expression $$8·2^{k-5}$$ equal to $$1$$?

   • $$0$$
   • $$2$$
   • $$5$$
   • $$-1$$

5. Which expression is equivalent to $$\frac{\sqrt[3]{x^{4}}}{x^{\frac{1}{2}}}?$$

   • $$x^{\frac{5}{6}}$$
   • $$x^{\frac{3}{4}}$$
   • $$x^{\frac{4}{3}}$$
   • $$x^{\frac{2}{3}}$$

6. If $$3^{4x+1}=27\cdot 9^{x},$$ what is the value of $$x?$$

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