Surds and Indices

  1. Solve the below equation and find the value of ?.

    (13)4 = ?
    1. 520
    2. 169
    3. 28561
    4. 14280
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    ? = √(13)4 = √13 x 13 x 13 x 13
    Apply the rule of square root.

    Correct Option: B

    ? = √(13)4 = √13 x 13 x 13 x 13
    Apply the rule of square root.
    = 13 x 13 = 169

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  1. 163/2 + 16 -3/2 = ?
    1. 0
    2. 4097/64
    3. 1
    4. 16/9097
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    163/2 + 16-3/2
    Apply the law of Fractional Exponents and Laws of Exponents
    am x an = am+n
    a-m = 1/am
    ⇒163/2 + 1/163/2

    Correct Option: B

    163/2 + 16-3/2
    Apply the law of Fractional Exponents and Laws of Exponents
    am x an = am+n
    a-m = 1/am
    ⇒163/2 + 1/163/2
    ⇒(161/2)3 + 1/(161/2)3
    ⇒(42 x 1/2)3 + 1/(42 x 1/2)3
    ⇒43 + 1/43
    ⇒ 64 + 1/64
    ⇒ (64 x 64+ 1)/64
    = (4096+1)/64
    = 4097/64

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  1. [(12)-2]2/[(12)2]-2 = ?
    1. 12
    2. 4.8
    3. 12/144
    4. 1
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    ? = [(12)-2]2/[(12)2]-2
    Apply the Algebra Law,
    (am)n = amn

    Correct Option: D

    ? = [(12)-2]2/[(12)2]-2
    Apply the Algebra Law,
    (am)n = amn

    = (12) - 4/(12) - 4
    = 1

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  1. (16)9 ÷ (16)4 x (16)3 = (16)?
    1. 6.75
    2. 8
    3. 10
    4. 12
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    Given that , (16)9 ÷ (16)4 x (16) 3 = (16)?

    Apply the law of Fractional Exponents and Laws of Exponents
    (am) x (an) = am + n-------------------1
    am ÷ an = am ? n----------------2

    Correct Option: B

    Given that ,(16)9 ÷ (16)4 x (16) 3 = (16)?
    Apply the law of Fractional Exponents and Laws of Exponents
    (am) x (an) = am + n-------------------1
    am ÷ an = am ? n----------------2
    ⇒ (16)9 ÷ (16)4 x (16) 3 = (16)?
    ⇒ (16)? = (16)9 + 3 - 4
    ? = 12 - 4 = 8

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  1. [ (11)3 x (6)2] ÷ (4)3 = ?
    1. 2994.75
    2. 748.6875
    3. 272.25
    4. 4492.125
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    ? = [ (11)3 x (6)2 ] x 1/43
    ? = [ 113 x 62 ] x 1/43
    Solve the equation by algebra law.

    Correct Option: B

    ? = [ (11)3 x (6)2 ] x 1/43
    ? = [ 113 x 62 ] x 1/43
    Solve the equation by algebra law.
    ?= [ 1331 x 36 ] x 1/64 =1331 x 36 / 64
    ? = 748.6875

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