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Quiz: Surds And Indices

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Number of Questions: 25

Question: 1 -

(5 - 7)2 * (6 - 9)2 / (23)-2 = ?

Options:

  1. 2382

  2. -2382

  3. 2304

  4. -2304

    5. Answer:

    2304
    Solution:

    (5 - 7)2 * (6 - 9)2 / (23)-2 = (-2)2 * (-3)2 * 1/(23)-2 

    = 4 * 9 * 64 = 2304.

Question: 2 -

(272/4-3)-5/6 = ?

Options:

  1. 1/46656

  2. 1/7256

  3. 1/1296

  4. 1/7776

    5. Answer:

    1/7776
    Solution:

    (272/4-3)-5/6 = [(33)2/(22)-3]-5/6 

    = (36 * 26)-5/6 
    = (66)-5/6 = 1/65 = 1/ 7776.

Question: 3 -

Simplify the following: 

(169/121)-3/2 * 27/2 * (13/22)-1

Options:

  1. 13-2 114 34

  2. 13-3 114 34

  3. 13-1 114 33

  4. 13-4 114 33

    5. Answer:

    13-4 114 33
    Solution:

    (169/121)-3/2 * 27/2 * (13/22)-1 

    (132/112)-3/2 * 27/2 * 22/13 = 13-3/11-3 * 27/2 * 22/13
    = 13-4 114 33 

Question: 4 -

(8x9 / 27y-6)-2/3 = ?

Options:

  1. 9/4 x-4 y-6

  2. 9/4 x-6 y-4

  3. 9/4 x-4 y6

  4. 9/4 x-6 y4

    5. Answer:

    9/4 x-6 y-4
    Solution:

    (8x9 / 27y-6)-2/3 = (8x9y6 / 27)-2/3 = [(2/3 x3 y2)3]-2/3 

    = 9/4 x-6 y-4.

Question: 5 -

(a-3 b-2 / a2 b2)-3 * (a3 b-4 / a-3 b3) / (a-2 b3/a-4 b-3) = ?

Options:

  1. a-19 b-1

  2. a-19 b

  3. a19 b

  4. a19 b-1

    5. Answer:

    a19 b-1
    Solution:

    (a-3 b-2 / a2 b2)-3 * (a3 b-4 / a-3 b3) / (a-2 b3/a-4 b-3) 

    = (a-5 b-4)-3 * a6b-7 / a2b6 
    = a15b12 * a6b-7 * a-2b-6 
    = a19 b-1