Question: 6 -

(9^-7 / 27^-3)^4/5 = ?

Options:

3^-4

3^-3

3^-2

3^-1

Answer:

3^-4

Solution:

(9^-7 / 27^-3)^4/5 = [(3²)^-7 / (3³)^-3]^4/5 

= (3^-14 3⁹)^4/5 = 3^-4 .

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Question: 7 -

(17¹⁴ * 17¹⁶) / 17^-8 = ?

Options:

17²⁸

17²⁴

17²⁶

17²²

Answer:

17²²

Solution:

? = 17^14+16-8 = 17²²

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Question: 8 -

(27^2/3 * 9^1/2 * 81^1/4)^-1/4 = ?

Options:

9

1/9

1/3

3

Answer:

1/3

Solution:

(27^2/3 * 9^1/2 * 81^1/4)^-1/4 = [(3³)^2/3 * (3²)^1/2 * (3⁴)^1/4]^-1/4 

= (3² * 3 * 3)^-1/4 = (3⁴)^-1/4 = 1/3.

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Question: 9 -

(3^-3 * 9^5/2) / (27^2/3 * 3^-4) = ?

Options:

9

21

3

81

Answer:

81

Solution:

(3^-3 * 9^5/2) / (27^2/3 * 3^-4) = [3^-3 * (3²)^5/2] / [(3³)^2/3 * 3^-4] 

= (3^-3 * 3⁵) / (3² * 3^-4) = (3^-3+5)/(3^2-4) = 3²/3^-2 = 3² * 3² = 81. 

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Question: 10 -

(3^a+1 9^a+2 27^a) / (3^a-1 9^a 27^a+1) = ?

Options:

3

27

1

9

Answer:

27

Solution:

(3^a+1 9^a+2 27^a) / (3^a-1 9^a 27^a+1) = [3^a+1 3^2(a+2) (3³)^a] / [3^a-1 (3²)^a (3³)^a+1] = 3^6a+5 / 3^6a+2 = 3³ = 27.

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