Solved Questions of Exponents
1. Simplify: (34)3 ÷ (32)5
a) 32
b) 35
c) 36
d) 311
Answer: a) 32
Explanation: When raising an exponent to another exponent, you multiply the exponents.
So, (34)3 ÷ (32)5
= 3(4x3) ÷ 3(2x5)
= 312 ÷ 310
= 312 - 10
= 32
2. Simplify: (53 x 62)2 ÷ (24 x 32)3
a) 212 x 56 ÷ 36
b) 212 x 36 ÷ 56
c) 56 x 2-8 x 3-2
d) 212 x 64 x 56
Answer: c) 56 x 2-8 x 3-2
Explanation: First simplify the exponents inside the parentheses:
(53 x 62)2 ÷ (24 x 32)3
= 56 x 64 ÷ (212 x 36)
= 56 x 24 x 34 x 2-12 x 3-6
= 56 x 24-12 x 34-6
= 56 x 2-8 x 3-2
3. Simplify: (82 x 2-3)-2 x 43
a) 213
b) 211
c) 2-1
d) 1
Answer: d) 1
Explanation: First simplify the exponents inside the parentheses. Then, simplify the expression outside the parentheses:
(82 x 2-3)-2 x 43
= (64 x 1/8)-2 x 64
= (8)-2 x 64
= (1/64) x 64
=1
4. What is the product of 32, 33 and 34?
a) 327
b) 39
c) 36
d) 354
Answer: b) 39
Explanation: When multiplying exponents with the same base, you add the exponents.
So, 32 x 33 x 34 = 3(2+3+4) = 39
5. What is the quotient of 68/619?
a) 6-11
b) 6-8
c) 60
d) 62
Answer: a) 6-11
Explanation: When dividing exponents with the same base, you subtract the exponents.
So, 68 ÷ 619 = 6(8 -19)
= 6-11
Practice Questions of Exponents
1. What is the product of 53 and 54?
a) 57
b) 512
c) 524
d) 534
Answer: a) 57
2. What is the quotient of 27 and 23?
a) 24
b) 210
c) 221
d) 243
Answer: a) 24
3. Evaluate: (43)5?
a) 48
b) 412
c) 415
d) 460
Answer: c) 415
4. Simplify: (4x3y4)2 ÷ (2xy2)3
a) 16x3y2
b) 2x3y2
c) 2y3
d) 8xy
Answer: b) 2x3y2
5. What is (2 x 106)3 expressed in scientific notation?
a) 8 x 1018
b) 8 x 1020
c) 8 x 1021
d) 8 x 1024
Answer: a) 8 x 1018
6. Simplify: (53 x 7-2)-2
a) 76 + 56
b) 56 x 36
c) 74 ÷ 56
d) 73 x 56
Answer: c) 74 ÷ 56
7. What is 5.7 x 108 + 2.4 x 107 expressed in scientific notation?
a) 6.05 x 108
b) 6.02 x 107
c) 5.94 x 108
d) 5.98 x 107
Answer: c) 5.94 x 108
8. What is (6 x 105) ÷ (3 x 103) expressed in scientific notation?
a) 2 x 102
b) 2 x 103
c) 2 x 104
d) 2 x 105
Answer: a) 2 x 102
9. What is 2.5 x 104 x 1.2 x 105 expressed in scientific notation?
a) 1.45 x 105
b) 1.45 x 106
c) 1.45 x 107
d) 1.45 x 108
Answer: a) 3.0 x 109
10. Simplify: (2x2y)3 ÷ (8x3y1)2
a) y7/16
b) 4x2y5
c) 4x5y3
d) y/8
Answer: d) y/8
