6. The positive exponential function of	a-3 a-4	is :
   	a-5

1. 1. a²

   
   
   

   2. 1

      a3

   
   
   

   3. 1

      a4

   
   
   

   4. 1

      a2

   
   
   

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1. View Hint View Answer Discuss in Forum

   a-3 a-4

   a-5

   
   

   =	a5	=	a5
   	a3 a4		a7

   
   

   =	1	=	1
   	a7 - 5		a2

   
   

   Correct Option: D

   a-3 a-4

   a-5

   
   

   =	a5	=	a5
   	a3 a4		a7

   
   

   =	1	=	1
   	a7 - 5		a2

   
   

   Therefore, positive exponential function of	a-3 a-4	will be	1
   	a - 5		a2

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7. If 10^2/5 × 10^8/5 = 10ⁿ, the value of n is :

1. 1. 2

   
   
   

   2. 3

   
   
   

   3. 6

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∵ 10^2/5 × 10^8/5 = 10ⁿ
   ⇒ 10^{2/5 + 8/5} = 10ⁿ
   ⇒ 10^10/5 = 10ⁿ

   Correct Option: A

   ∵ 10^2/5 × 10^8/5 = 10ⁿ
   ⇒ 10^{2/5 + 8/5} = 10ⁿ
   ⇒ 10^10/5 = 10ⁿ ⇒ 10² = 10ⁿ ⇒ n = 2
   Hence, the value of n is 2.

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8. The value of ( 8 ) ^{- ( 2 - 2 )} is :

1. 1. 	-	1
      2		4

   
   
   

   2. 	-	3
      2		4

   
   
   

   3. 	3
      2	4

   
   
   

   4. 	-	1
      2		2

   
   
   

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1. View Hint View Answer Discuss in Forum

   ( 8 ) ^{- ( 2 - 2 )} =

   	-	1
   8		4

   
   

   =	1
   		1
   	8	4

   
   

   =	1
   		1
   	( 2 x 2 x 2)	4

   
   

   Correct Option: B

   ( 8 ) ^{- ( 2 - 2 )} =

   	-	1
   8		4

   
   

   =	1
   		1
   	8	4

   
   

   =	1
   		1
   	( 2 x 2 x 2)	4

   
   

   =	1
   		3
   	2	4

   
   

   	-	3
   = 2		4

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9. The value of		-	1		- (2/3)
   			125

1. 1. 1

      25

   
   
   

   2. 25

   
   
   

   3. 5

   
   
   

   4. 1

      5

   
   
   

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1. View Hint View Answer Discuss in Forum

   The value of		-	1		- (2/3)
   			125

   
   

   =	1
   		-	1		- (2/3)
   			125

   
   

   	2
   = (- 125)	3

   
   

   Correct Option: B

   The value of		-	1		- (2/3)
   			125

   
   

   =	1
   		-	1		- (2/3)
   			125

   
   

   	2
   = (- 125)	3

   
   = [ ( - 125 )^1/3 ]² = [ (–5 × –5 × –5 )^1/3 ]²
   = (–5)² = – 5 × – 5 = 25

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10. The expression	( - 1 )132	is equivalent to :
    	5- 1 + 3- 1

1. 1. 16

      9

   
   
   

   2. -	15
      	8

   
   
   

   3. 15

      8

   
   
   

   4. 17

      8

   
   
   

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1. View Hint View Answer Discuss in Forum

   The expression	( - 1 )132	is equivalent to:
   	5- 1 + 3- 1

   
   

   =	[( - 1 )2]66
   	5- 1 + 3- 1

   
   

   =	( 1 )66
   	5- 1 + 3- 1

   
   

   =	1
   	1	+	1
   	5		3

   
   

   =	1
   	5 + 3
   	15

   
   

   Correct Option: C

   ( - 1 )132

   5- 1 + 3- 1

   
   

   =	[( - 1 )2]66
   	5- 1 + 3- 1

   
   

   =	( 1 )66
   	5- 1 + 3- 1

   
   

   =	1
   	1	+	1
   	5		3

   
   

   =	1
   	5 + 3
   	15

   
   

   =	1
   	8
   	15

   
   

   =	15
   	8

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