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Number System: Exponent Test-3

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Question 1

Which of the following expressions is equal to 2^{18} ?

A

(2^{3})^{6}

B

2^{9+2}

C

2^{3}2^{6}

D

9x2^{6}

Question 1 Explanation:

The correct expression in this case is option A. x^{mn }equals to (x^{m})^{n}

Question 2

What will be the value of P= 4^{a}+4^{a}+4^{a}+4^{a}

If q = {y(y^{2})^{4}} / y^{5} when y is greater than 0 then what would be the exponent of y.

A

2

B

3

C

4

D

5

Question 3 Explanation:

Since the question is to find the exponents of y in {y(y^{2})^{4}} / y^{5} Therefore
={y(y^{2})^{4}} / y^{5} ={y x y^{8}} / y^{5} ={y x y^{8}} / y^{5} = { y^{9}} / y^{5} = y^{4} So the exponent of y is 4

Question 4

If a and b are not equal to 0, then a^{18}b^{9 }must be

A

Positive

B

Negative

C

An integer

D

both A or B

Question 4 Explanation:

If a is negative and b is positive then the result will be positive If b is negative and a is positive then the result will be negative So we will consider both the cases and therefore the number can be positive of negative So the right answer is D

Question 5

If a and b are positive integers and a^{4} +b^{5} = 259, then value of a + b =?

A

7

B

9

C

6

D

5

Question 5 Explanation:

We have a^{4} +b^{5} = 259 So from option A = 7 so the value of A and B(1,6)(2,5)(3,4) and vice-versa but no one option satisfy the condition so option a is rejected For option B i.e.9 the pairs are (1,8), (2,6), (3,5), (4,4) and vice versa For option C i.e. for 6 the pairs are (1,5), (2,4), (3,3) and vice versa For option D i.e. for 5 the pairs are (1,4), (2,3), and vice versa See 2^{4} +3^{5} = 259 So the right answer is 5 option D

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