Surds and Indices Questions Answers

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

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

  Answer And Explanation

  Answer: Option B

  Explanation:

  $$\begin{aligned} = (256)^{\frac{5}{4}} = (4^4)^{\frac{5}{4}} = 4^5 = 1024 \end{aligned}$$

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

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

  Answer And Explanation

  Answer: Option C

  Explanation:

  $$\begin{aligned} = ((8)^\frac{1}{2})^\frac{1}{3} = 8^{(\frac{1}{2} \times \frac{1}{3})} \end{aligned}$$
  
  $$\begin{aligned} = (8)^{\frac{1}{6}} \end{aligned}$$
  
  $$\begin{aligned} = (2)^{3(\frac{1}{6})} \end{aligned}$$
  
  $$\begin{aligned} = (2)^{\frac{1}{2}} \end{aligned}$$

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• 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

  Answer And Explanation

  Answer: Option C

  Explanation:

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

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

  Answer And Explanation

  Answer: Option D

  Explanation:

  $$\begin{aligned} = \frac{(10)^{150}}{(10)^{146}} = 10^4 = 10000 \end{aligned}$$

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

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

  Answer And Explanation

  Answer: Option C

  Explanation:

  $$\begin{aligned} = \frac{(10^3)^7}{(10)^{18}} \end{aligned}$$
  
  $$\begin{aligned} = \frac{(10)^{21}}{(10)^{18}} = 10^3 = 1000 \end{aligned}$$

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• 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

  Answer And Explanation

  Answer: Option D

  Explanation:

  We know that $$\begin{aligned} (11)^2 = 121 \end{aligned}$$
  So, putting values in said equation we get,
  $$\begin{aligned} (11-1)^{2 + 1} = (10)^3 = 1000 \end{aligned}$$

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

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

  Answer And Explanation

  Answer: Option B

  Explanation:

  $$\begin{aligned} = 256^{0.16+0.09} = 256^{0.25} = 256^{\frac{25}{100}} \end{aligned}$$
  
  $$\begin{aligned} = 256^{\frac{1}{4}}= (4^4)^{\frac{1}{4}} \end{aligned}$$
  
  $$\begin{aligned} =(4)^{4 \times \frac{1}{4}} = 4 \end{aligned}$$

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