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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