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## Wednesday 24 February 2021

### CBSE Class 8 Maths - MCQ and Online Tests - Unit 12 - Exponents and Powers

#### CBSE Class 8 Maths – MCQ and Online Tests –  Unit 12 – Exponents and Powers

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#### CBSE Class 8 Maths – MCQ and Online Tests – Unit 12 – Exponents and Powers

Question 1.
(2° + 4-1) × 2² is equal to
(a) 2
(b) 3
(c) 4
(d) 5

Hint:
(20 + 4-1) × 2² = (1 + $$\frac{1}{4}$$) × 4 = $$\frac{5}{4}$$ × 4 = 5

Question 2.
32 x 42 is equal to:
(a) 121
(b) 49
(c) 144
(d) 156

Hint:
By exponent law;
am x bm = (ab)m
32 x 42 = (3×4)2 = 122 = 144

Question 3.
(2-1 + 3-1 + 5-1)0 is equal to
(a) 2
(b) 3
(c) 5
(d) 1.

Hint:
(2-1 + 3-1 + 5-1)0 = 1 [? a0 = 1]

Question 4.
3m + 3-3 = 35 ? m is equal to
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
3m + 3-3= 35 ? 3m+3 = 35
? m + 3 = 5 ? m = 2

Question 5.
am × bm is equal to
(a) (ab)m
(b) (ab)-m
(c) am b
(d) abm

Hint:
Formula

Question 6.
a0 is equal to
(a) 0
(b) 1
(c) -1
(d) a.

Hint:
Formula

Question 7.
$$\frac{a^m}{b^m}$$ is equal to bm
(a) ($$\frac{a}{b}$$)m
(b) ($$\frac{b}{a}$$)m
(c) ($$\frac{a^m}{b}$$)m
(d) ($$\frac{a}{b^m}$$)m

Answer: (a) ($$\frac{a}{b}$$)m
Hint:
Formula

Question 8.
2 × 2 × 2 × 2 × 2 is equal to
(a) 24
(b) 2³
(c) 2²
(d) 25

Hint:
Formula

Question 9.
In 10², the exponent is
(a) 1
(b) 2
(c) 10
(d) 1.

Hint:
Definition of exponent

Question 10.
In 10² the base is
(a) 1
(b) 0
(c) 10
(d) 100.

Hint:
Definition of base

Question 11.
10-1 is equal to
(a) 10
(b) -1
(c) $$\frac{1}{10}$$
(d) –$$\frac{1}{10}$$

Answer: (c) $$\frac{1}{10}$$
Hint:
10-1 = $$\frac{1}{10^1}$$ = $$\frac{1}{10}$$

Question 12.
The multiplicative inverse of 2-3 is
(a) 2
(b) 3
(c) 3
(d) 23

Hint:
2-3. 2³ = 2-3+3 = 20 = 1

Question 13.
The multiplicative inverse of 105 is
(a) 5
(b) 10
(c) 10-5
(d) 105.

Hint:
105. 10-5 = 25-5 = 100 = 1

Question 14.
The multiplicative inverse of $$\frac{1}{2^2}$$ is 22
(a) 25
(b) 2²
(c) 2
(d) 1.

Hint:
$$\frac{1}{2^2}$$ = 2² = 1

Question 15.
The multiplicative inverse of 1010 is
(a) 10
(b) $$\frac{1}{10}$$
(c) 10-10
(d) 1010.

Hint:
10-10.1010 = 10-10+10 = 100 = 1

Question 16.
The multiplicative inverse of am is
(a) a
(b) m
(c) am
(d) a-m

Hint:
Definition of multiplicative inverse

Question 17.
5³ × 5-1 is equal to
(a) 5
(b) 5³
(c) 5-1
(d) 5²

Hint:
5³ × 5-1 = 53-1 = 5²

Question 18.
(- 2)-5 x (-2)6 is equal to
(a) 2
(b) -2
(c) -5
(d) 6.

Hint:
(-2)-5 × (-2)6 = (-2)-5+6 = (-2)1 = -2

Question 19.
3² × 3-4 × 35 is equal to
(a) 3
(b) 3²
(c) 3³
(d) 35

Hint:
3² × 3-4 × 35 = 32-4+5 = 3³

Question 20.
(-2)-2 is equal to
(a) $$\frac{1}{4}$$
(b) $$\frac{1}{2}$$
(c) –$$\frac{1}{2}$$
(d) –$$\frac{1}{4}$$

Answer: (a) $$\frac{1}{4}$$
Hint:
(-2)-2 = $$\frac{1}{(-2)^2}$$ = $$\frac{1}{4}$$

Question 21.
($$\frac{1}{2}$$)-4 is equal to
(a) 2
(b) 2-4
(c) 1
(d) 2-4

Hint:
($$\frac{1}{2}$$)-4 = $$\frac{(1)^{-4}}{(2)^{-4}}$$ = $$\frac{1}{(2)^{-4}}$$ = 24

Question 22.
(-2)m+1 × (-2)4 = (-2)6 ? m =
(a) 0
(b) 1
(c) -1
(d) none of these.

Hint:
(-2)m+1 × (-2)4 = (-2)6
? (-2)m+1+4 = (-2)6
? m + 5 = 6 ? m = 1

Question 23.
57/67 will give the value:
(a) (5/6)7
(b) (5/6)0
(c) (5/6)-7
(d) (6/5)-7

Hint:
By exponent law:
am/bm = (a/b)m
57/67 = (?)7

Question 24.
1000+200+50 is equal to
(a) 125
(b) 25
(c) 1/125
(d) 3

Hint:
By exponent law we know:
a0 = 1
1000 + 200 + 50 = 1 + 1 + 1 = 3

Question 25.
If (–3)m+1 × (-3)5 = (-3)7, then the value of m is:
(a) 5
(b) 7
(c) 1
(d) 3

Explanation: (-3)m+1 × (-3)5 = (-3)7
(-3)m+1+5 = (-3)7
(-3)m+6 = (-3)7
Since, base are equal on both the sides, hence if we compare the powers,
m + 6 = 7
m = 7 – 6 = 1

Question 26.
(-1)50 is equal to
(a) -1
(b) 1
(c) 50
(d) – 50.

Hint:
(-1) even natural number = 1

Question 27.
(-1)51 is equal to
(a) -1
(b) 1
(c) 51
(d) -51.

Hint:
(-1) odd natural number = -1

Question 28.
149600000000 is equal to
(a) 1.496 × 1011
(b) 1.496 × 1010
(c) 1.496 × 1012
(d) 1.496 × 108.

Hint:
149,600,000,000 = 1.496 × 1011

Question 29.
300000000 is equal to
(a) 3 × 108
(b) 3 × 107
(c) 3 × 106
(d) 3 × 109

Hint:
300,000,000 = 3 × 108

Question 30.
0.000007 is equal to
(a) 7 × 10-6
(b) 7 × 10-5
(c) 7 × 10-4
(d) 7 × 10-3

Hint:
0.000007 = 7 × 10-6

Question 31.
384467000 is equal to
(a) 3.84467 × 108
(b) 3.84467 × 103
(c) 3.84467 × 107
(d) 3.84467 × 106

Hint:
384467000 = 3.84467 × 108

Question 32.
0.00001275 is equal to
(a) 1.275 × 10-5
(b) 1.275 × 10-3
(c) 1.275 × 104
(d) 1.275 × 103

Hint:
0.00001275 = 1.275 × 10-5

Question 33.
am x am is equal to
(a) am+n
(b) am-n
(c) amn
(d) an-m

Hint:
Formula

Question 34.
am ÷ an is equal to
(a) am-n
(b) am+n
(c) amn
(d) an-m

Hint:
Formula

Question 35.
(am)n is equal to
(a) am+n
(b) am-n
(c) amn
(d) an-m

Hint:
Formula

Question 36.
0.0016 is equal to
(a) 1.6 × 10-3
(b) 1.6 × 10-2
(c) 1.6 × 10-4
(d) 1.6 × 10-5

Hint:
0.0016 = 1.6 × 10-3

Question 37.
0.000003 is equal to
(a) 3 × 10-6
(b) 3 × 106
(c) 3 × 105
(d) 3 × 10-5

Hint:
0.000003 = 3 × 10-6

Question 38.
8848 is equal to
(a) 8.848 × 103
(b) 8.848 × 10²
(c) 8.848 × 10
(d) 8.848 × 104

Hint:
8848 = 8.848 × 10³

Question 39.
1.5 × 1011 is equal to
(a) 150000000000
(b) 15000000000
(c) 1500000000
(d)1500000000000.

Hint:
1.5 × 1011 = 150,000,000,000

Question 40.
2.1 × 10-6 is equal to
(a) 0.0000021
(b) 0.000021
(c) 0.00021
(d) 0.0021.

Hint:
2.1 × 10-6 = 0.0000021

Question 41.
2.5 × 104 is equal to
(a) 25
(b) 250
(c) 2500
(d) 25000.

Hint:
2.5 × 104 = 25000

Question 42.
0.07 × 1010 is equal to
(a) 700000000
(b) 7000000
(c) 7000
(d) 7.

Hint:
0.07 × 1010 = 700,000,000.

Question 43.
The value of 2-2 is:
(a) 4
(b) ¼
(c) 2
(d) ½

Hint:
2-2 = 1/22 = ¼

Question 44.
The multiplicative inverse of 7-2 is:
(a) 72
(b) 7
(c) 1/72
(d) 1/7

Hint:
The multiplicative inverse of any value is the one which when multiplied by the original value gives a value equal to 1.
7-2 = 1/72
Hence, 72 x 1/72 = 1

Question 45.
22 x 23 x 24 is equal to:
(a) 224
(b) 2-5
(c) 29
(d) 2-9

Hint:
By laws of exponents:
am x an = am+n
22 x 23 x 24 = 22+3+4 = 29

Question 46.
3-2 x 3-5 is equal to:
(a) 3-7
(b) 3-3
(c) 3-10
(d) 37

Hint:
3-2 x 3-5 = (1/32) x (1/35)
= (1/32+5)
= (1/37)
= 3-7

Question 47.
54/52 is equal to:
(a) 56
(b) 5-6
(c) 5-2
(d) 52

Hint:
By exponent law:
am/an = am-n
54/52 = 54-2 = 52

Question 48.
The value of (34)3 is:
(a) 3
(b) 312
(c) 37
(d) None of the above

Hint:
By law of exponent:
(am)n = amn
(34)3 = 34×3 = 312

Question 49.
695000 is equal to
(a) 6.95 × 105
(b) 6.95 × 103
(c) 6.95 × 106
(d) 6.95 × 104

Hint:
695000 = 6.95 × 105

Question 50.
503600 is equal to
(a) 5.036 × 105
(b) 5.036 × 106
(c) 5.036 × 104
(d) 5.036 × 107