CBSE Class 7 Mathematics Exponents And Powers Worksheet Set 03

Question. Evaluate: (16/81)^3/4
(A) 9/2
(B) 2/9
(C) 8/27
(D) 27/8
Answer : C

Question. What is the value of (512)^-2/9?
(A) 1/2
(B) 2
(C) 4
(D) 1/4
Answer : D

Question. Simplify (32)^-2/5 + (125)-^2/3.
(A) 4/25
(B) 25/4
(C) 2/5
(D) 5/2
Answer : B

Question. If x^Y = y^x, find the value of (x/y)^x/y
(A) X^x/Y
(B) X^{x/Y - 1}
(C) X^y/x 
(D) X^{y/x - 1}
Answer : B

Question. Evaluate (5)^0.25 X (125)^0.25/( 256)⁰¹⁰ x (256)^0.15 .
(A) √5/2
(B) 5/4
(C) 25/2
(D) 25/16
Answer : B

Question. What is the value of (67.542)² - (32.458)² / 75.458 - 40.374 ?.
(A) 1
(B) 10
(C) 100
(D) -10
Answer : C

Question. Which of the following values are equal?
I. 14 II. 4°
Ill. 04 IV. 41
(A) I and II
(B) II and Ill
(C) I and Ill
(D) I and IV
Answer : A

Question. Find the sum of the powers of the prime factors in 108 x 192.
(A) 5
(B) 7
(C) 8
(D) 12
Answer : D

Question. What is the value of (3°- 4°) X 5^-3?
(A) 25
(B) 0
(C) -25
(D) -125
Answer : B

Question. What is the solution of 3^3x-5 = 1/9X ?
(A) 5/2
(B) 5
(C) 1
(D) 7/3
Answer : C

Question. Find the value of [(- 3)^{( -2)}]^(-3)
(A) 729
(B) 32
(C) 64
(D) -729
Answer : A

Question. Compute (64)^-1/6 x (216)^-1/3 x (81)^1/4 / (512)^-1/3 x (16)^1/4 x (9)^-1/2
(A) 3
(B) 6
(C) 1
(D) -6
Answer : A

Question. Find the value of 3³√2 X 7³√6 X 5³√18.
(A) 545
(B) 500
(C) 630
(D) 360
Answer : C

Question. Find the value of (-3)⁰ - (- 3)³ - (- 3)^-1 +(-3)⁴ -(-3)^-2.
(A) 109(2/9)
(B) 102(2/9)
(C) 109
(D) 110
Answer : A

Question. Evaluate 

(A) 3(173/440)
(B) 3(17/44)
(C) 3(137/322)
(D) 3(21/440)
Answer : A

Question. What is the simplified form of

Answer : B

Question. If 3ⁿ = 729, find the value of 3³ⁿ + 1.
(A) 3²¹
(B) 3¹⁰
(C) 3¹⁹
(D) 3¹⁵
Answer : C

Question. If 27^{x + 1} = 9^{x + 3} = 3^Y, find the respective values of 'x' and y
(A) 3 and 12
(B) 12 and 3
(C) 6 and 6
(D) 4 and 9
Answer : A

Question. Find (0.000064) 514 x (0.04)514.
(A) 2¹⁰.10¹⁰
(B) 2¹⁰.10^-10
(C) 2^-10.10¹⁰
(D) 2^-10 10^-10
Answer : B

Question. Find the value of 1/1+x +1/1+x^m
(A) 0
(B) x^m
(C) 1
(D) x^-m
Answer : C

Question. Give the simplified form of 3^a 4^a-2 25^a+1 / 9^a-12^a+15^a-2
(A) 3^a-2 . 2^a-5 . 5^a+4
(B) 2^a-s . 3^a+2 . 5^a+4
(C) 2^a+5 . 3^-a+2. 5^a+4
(D) 2^a-5 . 3^-a+2 . 5^a+4
Answer : B

Question. Which is greater of 2¹² and 3⁸?
(A) 3⁸
(B) 2¹²
(C) Both are equal.
(D) Cannot be compared.
Answer : A

Question. What is the simplified form of (X^a+b)³ . (X^b+c)³ . (X^c+a)³/(X^a . X^b . X^c) ?
(A) 0
(B) 1
(C) X^a+b+c
(D) X
Answer : B

Question. By what number should we multiply 4^-3 so that the product may be equal to 64?
(A) 4⁵
(B) 2¹²
(C) 2⁶
(D) 1
Answer : B

Question. What is the number to be multiplied by (-7)^-1 so as to get 10-1 as the product?
(A) -7/10
(B) 7/10
(C) 9/10
(D) -3/10
Answer : A

Question. What is the value of (6^-1- 8^-1) + (2^-1- 3^-1)^-1?
(A) 25
(B) 30
(C) 35
(D) 40
Answer : B

Question. If (25)^x = (125)^Y, find X : y.
(A) 1 : 1
(B) 2 : 3
(C) 3 : 2
(D) 1 : 3
Answer : C

Question. What is the standard form of 6020000000000000?
(A) 6.02 X 10¹⁵
(B) 6.02 X 10¹³
(C) 602 X 10¹³
(D) 602 X 10^-15
Answer : A

Question. What is the usual form of 1.0001 x 1 09?
(A) 100010000
(B) 1000100000
(C) 10001000000000
(D) 10001000000
Answer : B

Question. The size of a plant cell is 0.0000127 5 m .
Express this size in standard form.
(A) 1.25 X 10⁸ m
(B) 1.275 x 10⁵ m
(C) 1.275 x 10^-8 m
(D) 1.275 x 10^-5 m
Answer : D

Question. Evaluate {(3/4)^-1 (1/4)^-1}^-1
(A) 3/16
(B) -3/8
(C) 16/3
(D) -8/3
Answer : B

Question. A box has 5 books, each 20 mm thick and 5 cards each 0.016 mm thick. What is the total thickness?
(A) 1.0008 x 10⁴ mm
(B) 1.008 x 10³ mm
(C) 1.0008 x 10² mm
(D) 1.0008 x 10⁵ mm
Answer : C

Question. The size of a red blood cell is 0.000007 m.
The size of a plant cell is 0.0000127 5 m.
Compare them.
(A) 2
(B) 4
(C) 5
(D) -5
Answer : A

Question. By what number should (-8)^-1 be divided to get 10^-1?
(A) 4/5
(B) -5/4
(C) -4/5
(D) 5/4
Answer : B

Mark tick against the correct answer in each of the following:

1. (6-1– 8-1)-1 =?
(a) (-1/2) (b)-2 (c) (1/24) (d) 24
Solution:- (D) 24
We know that, = (6)-1= (1/6)1 … [∵ (a/b)^-n
= (b/a) n] = (8)^-1
= (1/8)¹ … [∵ (a/b)^-n
= (b/a) ⁿ] Now subtract,
= {(1/6) – (1/8)}^-1
= {(4-3)/24}^-1 … [LCM of 6 and 8 is 24]
= {1/24}^-1
= {24/1} = 24

2. (5^-1 × 3 ^-1)^-1
(a)(1/15) (b)(-1/15) (c) 15 (d)-15
Solution:- (c)15
We know that,
= (5)^-1= (1 /5)¹ … [∵ (a/b)^-n
= (b/a) ⁿ] = (3)^-1 
= (1/3)¹ … [∵ (a/b)^-n
= (b/a) ⁿ] Now multiply,
= {(1/5) × (1/3)}^-1 
= {(1×1)/ (5×3)}^-1
= {1/15}^-1
= {15/1}
= 15

3. (2^-1 – 4^-1)² (a) 4 (b)-4 (c) (1/16) (d) (-1/16)
Solution:- (c) (1/16)
We know that, = (2)^-1
= (1/2)¹ … [∵ (a/b)^-n
= (b/a) ⁿ]
= (4)^-1
= (1/4)1 … [∵ (a/b)^-n 
= (b/a) ⁿ]
Now subtract,
= {(1/2) – (1/4)} ²
= {(2-1)/4}² … [LCM of 2 and 4 is 4]
= {1/4}²
= {1²/4²}
= {1/16}

4. (1/2)^-2 + (1/3)^-2 + (1/4)^-2 =?
(a)(61/144) (b) 29 (c) (144/61) (d) none of these
Solution:- (b) 29
We know that,
= (1/2)^-2= (2/1)² … [∵ (a/b)^-n = (b/a) ⁿ]
= (1/3)^-2
= (3/1)² … [∵ (a/b)^-n = (b/a) ⁿ]
= (1/4)^-2 = (4/1)² … [∵ (a/b)^-n
= (b/a) ⁿ] Now add,
= (2)²+ (3)²+ (4)²
= 4 + 9 + 16
= 29

5.{6^-1+(3/2)^-1}^-1
(a)(2/3) (b)(5/6) (c)(6/5) (d) None of these
Solution:- (c)(6/5)
We know that, = (6)^-1
= (1/6) … [∵ (a/b)^-n
= (b/a) ⁿ]
= (3/2)^-1
= (2/3) … [∵ (a/b)^-n
= (b/a) ⁿ] Now add,
= {(1/6) + (2/3)^}-1
= {(1+4)/ 6}^-1 … [LCM of 6 and 3 is 6]
= {5/6}^-1
= {6/5}

6. (-1/2)^-6 =?
(a)-64 (b) 64 (c) (1/64) (d) (-1/64)
Solution:- (b) 64
We know that,
= (-1/2)^-6
= (-2/1)⁶ … [∵ (a/b)^-n= (b/a) ⁿ]
= (-2)⁶ = 64

7. {(3/4)^-1 – (1/4)^-1}^-1=?
(a)(3/8) (b)(-3/8) (c)(8/3) (d)(-8/3)
Solution:- (b)(-3/8) We know that,
= (3/4)^-1
= (4/3)¹ … [∵ (a/b)^-n = (b/a) ⁿ]
= (1/4)^-1
= (4/1)¹ … [∵ (a/b)^-n = (b/a) ⁿ]
Now subtract,
= {(4/3) – (4/1)} ^-1
= {(4-12)/3}^-1 … [LCM of 3 and 1 is 3]
= {-8/3}^-1 = {-3/8}

8. [{(-1/2)²}^-2]^-1=?
(a) (1/16) (b)16 (c)(-1/16) d)-16
Solution:- (a) [{(-1/2)²}^-2]^-1
= [{(-1²/2²)}^-2]^-1
= [{1/4}^-2]^-1
= [{4} ²]^-1
= [16]^-1
= [1/16]

9. (5/6)⁰ =?
(a) 5/6 (b) 0 (c)1 (d)none of these
Solution:- (c) (5/6)⁰
=1 By definition,
we have a⁰= 1 for every integer.

10. (2/3)^-5=?
(a)(32/243) (b)(243/32) (c)(-32/243) (d)(-243/32)
Solution:- (b) (2/3)^-5
= (3/2)⁵
= (3⁵/2⁵)
= (243/32)

Please click the below link to access CBSE Class 7 Maths Worksheet - Exponents & Powers (3)