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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}

  • 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}

  • 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

  • 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}

  • 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}

  • 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}

  • 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}