Chapter 8. Exponents and Powers

Example 1:Multiplicative inverse of 27 is
(a)2–7(b)72(c)– 27(d)– 27
Solution:The Correct answer is (a).
Example 2:The human body has about 100 billion cells. This number

can be written in exponential form as
(a)10–11(b)1011(c)109(d)10–9
Solution:The correct answer is (b).

1.In 2n, n is known as
(a)Base(b)Constant(c)x(d)Variable
2.For a fixed base, if the exponent decreases by 1, the number becomes
(a)One-tenth of the previous number.
(b)Ten times of the previous number.
(c)Hundredth of the previous number.
(d)Hundred times of the previous number.
3.3–2 can be written as
(a)32(b)21/3(c)21/3−(d)2/3−
4.The value of 2 1/4− is
(a)16(b)8(c)1/16(d)1/8

5.The value of 35 ÷ 3–6 is
(a)35(b)3–6(c)311(d) 3–11
6.The value of
22
5
−

    is
(a) 4
5(b) 4
25(c) 25
4(d) 5
2
7.The reciprocal of
–12
5

    is
(a) 2
5(b) 5
2(c) –5
2(d) –2
5
8.The multiplicative inverse of 10–100 is
(a) 10(b) 100(c) 10100(d) 10–100
9.The value of (–2)2×3 –1 is
(a) 32(b) 64(c) – 32(d) – 64
10.The value of 423 is equal to
(a) 16/81(b) 81/16(c) 16/81−(d) 81/16

11.The multiplicative inverse of
995
9
−

 −    is
(a)
995
9

 −    (b)
995

9

    (c)
999
5

   −  (d)
999

5

   
12.If x be any non-zero integer and m, n be negative integers, then
xm × xn is equal to
(a) xm(b) xm+n(c) xn(d) xm–n
13.If y be any non-zero integer, then y0 is equal to
(a) 1(b) 0(c) – 1(c) Not defined
14.If x be any non-zero integer, then x–1 is equal to
(a) x(b) 1
x(c) – x(c) 1
x
−
15.If x be any integer different from zero and m be any positive integer,
then x–m is equal to
(a) xm(b) –xm(c) 1mx(d) 1mx
−
16. If x be any integer different from zero and m, n be any integers, then
(xm)n is equal to
(a) xm+n(b) xmn(c) m
nx(d) xm–n
17.Which of the following is equal to
–33
4

 −    ?
(a)
–33

4

    (b) –
–33

4

    (c)
34
3

    (d)
34
3

 −   
18.
–55
7

 −    is equal to
(a)
–55
7

    (b)
55
7

    (c)
57
5

    (d)
57
5
−
12/04/18

252     SMELBORP RALPMEXE
SCITAMEHTAM
19.
–17
5
−
     is equal to
(a) 5
7(b) –5
7(c) 7
5(d) 7
5
−
20.(–9)3 ÷ (–9)8 is equal to
(a) (9)5(b) (9)–5(c) (– 9)5(d) (– 9)–5
21.For a non-zero integer x, x7 ÷ x12 is equal to
(a) x5(b) x19(c) x–5(d) x–19
22.For a non-zero integer x, (x4)–3 is equal to
(a) x12(b) x–12(c) x64(d) x–64
23.The value of (7–1 – 8–1)–1 – (3–1 – 4–1)–1 is
(a) 44(b) 56(c) 68(d) 12
24.The standard form for 0.000064 is
(a) 64 × 104(b) 64 × 10–4(c) 6.4 × 105(d) 6.4 × 10–5
25.The standard form for 234000000 is
(a) 2.34 × 108(b) 0.234 × 109(c) 2.34 × 10–8(d) 0.234×10–9
26.The usual form for 2.03 × 10–5
(a) 0.203(b) 0.00203(c) 203000 (d) 0.0000203

27.0110 is equal to
(a) 0(b) 1/10(c) 1(d) 10
28. 5535 43 is equal to
(a) 535/43     (b) 135/43   (c) 035/43   (d)  1035/43
29.For any two non-zero rational numbers x and y, x4 ÷ y4 is equal to
(a) (x ÷ y)0(b) (x ÷ y)1(c) (x ÷ y)4(d) (x ÷ y)8
30.For a non-zero rational number p, p13 ÷ p8 is equal to
(a) p5(b) p21(c) p–5(d) p–19
31.For a non-zero rational number –23,()zz is equal to
(a) z6(b) z–6(c)z1(d) z4
32.Cube of 1/2− is
(a) 1/8(b) 1/16(c) 1/8−(d) 1/16−
33.Which of the following is not the reciprocal of 423   ?
(a) 43/2       (b) 43/2−      (c) 42/3−(d)4432
Fill in the blanks to make the statements true.
34.The multiplicative inverse of 1010 is ___________.
35.a3 × a–10 = __________.
36.50 = __________.
37.55 × 5–5 = __________.
38.The value of 2312 is equal to _________.
39.The expression for 8–2 as a power with the base 2 is _________.
40.Very small numbers can be expressed in standard form by using _________ exponents.
41.Very large numbers can be expressed in standard form by using _________ exponents.
42.By multiplying (10)5 by (10)–10 we get ________.
43. 3–63–9222_______131313
44.Find the value [4–1 +3–1 + 6–2]–1.
45.[2–1 + 3–1 + 4–1]0 = ______
46.The standard form of 1/100000000 is ______.
47.The standard form of 12340000 is ______.
48.The usual form of 3.41 × 106 is _______.
49.The usual form of 2.39461 × 106 is _______.
50.If 36 = 6 × 6 = 62, then 1/36expressed as a power with the base 6 is ________.

51.By multiplying 45/3 by ________ we get 54.
52.35 ÷ 3–6 can be simplified as __________.
53.The value of 3 × 10 ̄7 is equal to ________.
54.To add the numbers given in standard form, we first convert them into numbers with __ exponents.
55.The standard form for 32,50,00,00,000 is __________.
56.The standard form for 0.000000008 is __________.
57.The usual form for 2.3 × 10-10 is ____________.
58.On dividing 85 by _________ we get 8.
59.On multiplying _________ by 2–5 we get 25.
60.The value of [3–1 × 4–1]2 is _________.
61.The value of [2–1 × 3–1]–1 is _________.
62.By solving (60 – 70) × (60 + 70) we get ________.
63.The expression for 35 with a negative exponent is _________.
64.The value for (–7)6 ÷ 76 is _________.
65.The value of [1–2 + 2–2 + 3–2] × 62 is _______