Surds and Indices


  1. If 3x - 3x-1 = 18, then xx is equal to









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    ∵ 3x - 3x - 1 = 18
    ⇒ 3x - 1(3 - 1) = 18
    Apply the Algebra law,
    If aX = aY then X will be equal to Y.
    means X = Y;

    Correct Option: C

    ∵ 3x - 3x - 1 = 18
    ⇒ 3x - 1(3 - 1) = 18
    ⇒ 3x - 1(2) = 18
    ⇒ 3x - 1 = 18/2
    ⇒ 3x - 1 = 9
    ⇒ 3x - 1 = 32
    Apply the Algebra law,
    If aX = aY then X will be equal to Y.
    means X = Y;
    ⇒ x - 1 = 2
    ⇒ x = 3
    Then xx = (3)3 = 27


  1. If a2x + 2 = 1,where a is a positive real number other than 1, then x = ?









  1. View Hint View Answer Discuss in Forum

    Given that, a2x + 2 = 1
    Apply the algebra Law,
    p0 = 1
    and if
    pX = pY
    then X will be equal to Y. means X = Y;

    Correct Option: B

    Given that, a2x + 2 = 1
    Apply the algebra Law,
    p0 = 1

    ⇒ a2x + 2 = a0
    Apply the algebra law
    pX = pY then X will be equal to Y. means X = Y;

    ⇒ 2x + 2 = 0
    ⇒ x = -2/2 = -1



  1. Value of ? in expression
    78.9 ÷ (343)1.7 x (49)4.8 = 7? is











  1. View Hint View Answer Discuss in Forum

    78.9 ÷ (343)1.7 x (49)4.8 = 7?
    Apply the law of Fractional Exponents and Laws of Exponents
    (am)(an) = am+n
    am÷an=am?n
    am/an=am?n
    (am)n = amn

    Correct Option: A

    78.9 ÷ (343)1.7 x (49)4.8 = 7?
    Apply the law of Fractional Exponents and Laws of Exponents
    (am)(an) = am+n
    am÷an=am?n
    am/an=am?n
    (am)n = amn
    78.9 ÷ (343)1.7 x (49)4.8 = 7?
    ⇒ 78.9 ÷ (73)1.7 x (72)4.8 = 7?
    ⇒ 78.9 ÷ 75.1 x 79.6 = 7?
    ⇒ 78.9 - 5.1 + 9.6 = 7?
    ⇒ 718.5 - 5.1 = 7?
    ∴ ? = 13.4


  1. If 10 + ∛ x = 4, then what is the value of x ?









  1. View Hint View Answer Discuss in Forum

    Given, √10 + ∛ x = 4
    On squaring both sides,
    After squaring the both sides,
    Now, cubic on both sides,
    Then solve the equation.

    Correct Option: B

    Given, √10 + ∛ x = 4
    On squaring both sides, we get
    10 + ∛x = 16
    ⇒ ∛x = 6
    Now, cubic on both sides, we get
    x = (6)3 = 216



  1. If {(24)1/2}? = 256, find the value of '?'.











  1. View Hint View Answer Discuss in Forum

    Given that, (24x 1/2)? = 256
    Apply the law of Fractional Exponents and Laws of Exponents
    (am)n = am x n ----------------1
    (am) x (an) = am + n-------------------2
    am ÷ an = am ? n----------------3
    and if pX = pY then X will be equal to Y. means X = Y;----------------4

    Correct Option: C

    Given that, (24x 1/2)? = 256
    Apply the law of Fractional Exponents and Laws of Exponents
    ⇒ (22)? = 28
    ⇒ 22 x ? = 28
    ⇒ 2 x ? = 8
    ∴ ? = 8/2 = 4