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Quiz: Surds And Indices

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Number of Questions: 25

Question: 11 -

If 34m+1 = 37m-5, solve for m.

Options:

  1. 2

  2. 3

  3. 1/2

  4. 1/3

    5. Answer:

    2
    Solution:

    34m+1 = 37m-5 equating powers of 3 on both sides, 4m+1 = 7m - 5 => 3m = 6 => m = 2.

Question: 12 -

If 24m+2 = 46m-4, solve for m.

Options:

  1. 7/4

  2. 2

  3. 5/4

  4. 3

    5. Answer:

    5/4
    Solution:

    24m+2 = 46m-4 = 24m+2 = (22)6m-4 => 24m+2 = 2212m-8 Equating powers of 2 both sides. 

    4m + 2 = 12m - 8 => 10 = 8m => m = 5/4.

Question: 13 -

Solve for m if 36 (6m) = (216)3m+4

Options:

  1. -11/4

  2. -5/4

  3. -9/4

  4. -7/4

    5. Answer:

    -5/4
    Solution:

    36 (6m) = (216)3m+4 => 62 6m = (63)3m+4 => 62+m = 69m+12 Equating powers of 6 on both sides. 

    m + 2 = 9m + 12 => -10 = 8m => m = -5/4

Question: 14 -

Simplify : (y4b-a . y4c-b . y4a-c) / (ya . yb . yc)3

Options:

  1. 1

  2. y2

  3. 0

  4. y

    5. Answer:

    1
    Solution:

    (y4b-a . y4c-b . y4a-c) / (ya . yb . yc)3 

    = (y4b-a . y4c-b . y4a-c) / (ya+b+c)3 
    = y4b-a+4c-b+4a-c / y3(a+b+c) 
    = y3(a+b+c) / y3(a+b+c) = 1.

Question: 15 -

Simplify : 1 - {1 + (a2 - 1)-1}-1 

Options:

  1. a2

  2. -a2

  3. -1/a2

  4. 1/a2

    5. Answer:

    1/a2
    Solution:

    1 - {1 + (a2 - 1)-1}-1 = 1 - {1 + 1/a2 - 1}-1 = 1 - {a2 / a2 - 1}-1 = 1 - (a2 - 1)/a2 = 1/a2.