Surds and Indices Questions Answers Online Quiz Test

• 1. Value of $$\begin{aligned} (256)^{\frac{5}{4}} \end{aligned}$$

  1. 1012
  2. 1024
  3. 1048
  4. 525

• 2. $$\begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}$$

  1. 2
  2. 4
  3. $$\begin{aligned} \sqrt{2} \end{aligned}$$
  4. 8

• 3. Find the value of,
  $$\begin{aligned} \frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}} \end{aligned}$$

  1. 100
  2. 101
  3. 102
  4. 103

• 4. Find the value of
  $$\begin{aligned} (10)^{150} \div (10)^{146} \end{aligned}$$

  1. 10
  2. 100
  3. 1000
  4. 10000

• 5. $$\begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}$$

  1. 10
  2. 100
  3. 1000
  4. 10000

• 6. If m and n are whole numbers such that
  $$\begin{aligned} m^n=121 \end{aligned}$$
  , the value of $$\begin{aligned} (m-1)^{n + 1} \end{aligned}$$ is

  1. 1
  2. 10
  3. 100
  4. 1000

• 7. Evaluate $$\begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}$$

  1. 2
  2. 4
  3. 8
  4. 16

• 8. $$\begin{align} \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?} \end{align}$$

  1. 1.5
  2. 4.5
  3. 7.5
  4. 9.5

• 9. $$\begin{aligned} \text{If }x = \left(8 + 3\sqrt{7}\right),\text{ what is the value of }\\\left(\sqrt{x} - \dfrac{1}{\sqrt{x}}\right)? \end{aligned}$$
  

  1. $$\begin{aligned} \sqrt{13} \end{aligned}$$
  2. $$\begin{aligned} \sqrt{14} \end{aligned}$$
  3. $$\begin{aligned} \sqrt{15} \end{aligned}$$
  4. $$\begin{aligned} \sqrt{16} \end{aligned}$$

• 10. $$\begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2 \end{aligned}$$

  1. 25
  2. 28
  3. 36
  4. 44

• 11. $$\begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}$$
  

  1. $$\begin{aligned} \frac{5}{2} \end{aligned}$$
  2. $$\begin{aligned} \frac{2}{5} \end{aligned}$$
  3. $$\begin{aligned} \frac{3}{5} \end{aligned}$$
  4. $$\begin{aligned} \frac{5}{3} \end{aligned}$$

• 12. $$\begin{aligned} x = 3 + 2\sqrt{2}, \text{ then the value of }\\ (\sqrt{x} - \frac{1}{\sqrt{x}}) \end{aligned}$$

  1. 1
  2. 2
  3. 3
  4. 4

• 13. $$\begin{aligned} \frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ? \end{aligned}$$

  1. 1
  2. 2
  3. 3
  4. 4

• 14. $$\begin{aligned} \text{If } 3^{x-y} = 27 \text{ and } 3^{x+y} = 243, \\ \text{ then find the value of x } \end{aligned}$$

  1. 1
  2. 2
  3. 3
  4. 4

• 15. $$\begin{aligned} \text{if }6^m = 46656, \\\text{ What is the value of }6^{m-2} \end{aligned}$$

  1. 7776
  2. 7782
  3. 1296
  4. 1290

• 16. $$\begin{aligned} \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^? \end{aligned}$$

  1. 9.7
  2. 11.5
  3. 12
  4. 13