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Number System: Exponent Test-4

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Question 1

If 2^{3x }= 64 and 3^{√y} = 81 then what will be the value of {(3^{x-1})3^{-2}} / 1/3^{y}

A

3/y

B

3^{15}

C

45

D

None

Question 1 Explanation:

2^{3x }= 64 2^{3x }= 2^{6} 3x = 6 x = 2 now 3^{√y} = 81 3^{√y} = 3^{4} √y = 4 y = 16 Therefore the value of {(3^{x-1})3^{-2}} / 1/3^{16} {3^{1} x 1/9 } / 1/3^{16} = 3^{15} so option B

Question 2

What will be the value of {a^{-2}/y^{6 }} x (a^{-4}y^{-6}/z^{3})^{4}

A

a^{-18 }y^{-30} z^{-12}

B

a^{-14} y^{-30} z^{-12}

C

a^{-14} y^{-30} z^{-10}

D

None

Question 2 Explanation:

= {a^{-2}/y^{6 }} x (a^{-4}y^{-6}/z^{3})^{4} = {a^{-2}y^{-6 }} x (a^{-4}y^{-6}z^{-3})^{4} = {a^{-2}y^{-6 }} x (a^{-12}y^{-24}z^{-12}) = (a^{-18 }y^{-30 }z^{-12}) So option A

Question 3

What will be the exponent value of 2 value of {5^{4} a^{3}/2^{4} b^{0}}^{3} {4^{-3} a^{-2}/5^{3} b}^{-3}

A

18

B

12

C

6

D

none

Question 3 Explanation:

{5^{4} a^{3}/2^{4} b^{0}}^{3} {4^{-3} a^{-2}/5^{3} b}^{-3} ={5^{4} a^{3} 2^{-4} b^{0}}^{3} {4^{-3} a^{-2} 5^{-3} b}^{-3} = {5^{20} a^{9} 2^{-12} b^{0}} {4^{9} a^{6} 5^{9} b} ={5^{20} a^{9} 2^{-12} b^{0}} {2^{18} a^{6} 5^{9} b} = the exponent of 2 from here is 6
So option C is the right answer