Q1Written answer
Evaluate:
(i) 3-2 (ii) (-4)-2 (iii) (1/2)-5
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Worked solution
(i) 3-2 = (1/3)2
= 1/9
(ii) (-4)-2 = (1/-4)2
= 1/16
(iii) (1/2)-5 = (2/1)5
= 25
= 32
NCERT · Class 8 · Maths
Chapter 12: Exponents and Powers
Practice each question, then open the answer or worked solution.
Exercise 12.1
7 questionsQ2Written answer
Simplify and express the result in power notation with a positive exponent:
(i) (-4)4 ÷(-4)8
(ii) (1/23)2
(iii) -(3)4×(5/3)4
(iv) (3-7÷3-10)×3-5
(v) 2-3×(-7)-3
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Worked solution
(i)
= (-4)5/(-4)8
= (-4)5-8
= 1/(-4)3
(ii) (1/23)2
= 12/(23)2
= 1/23×2 = 1/26
(iii) -(3)4×(5/3)4
= (-1)4×34×(54/34 )
= 3(4-4)×54
= 30×54 = 54
(iv) 
= (3-7/3-10)× 3-5
= 3-7 – (-10) × 3-5
= 3(-7+10)×3-5
= 33×3-5
= 3(3+-5)
= 3-2
=1/32
(v) 2-3×(-7) – 3
= (2×-7)-3
(Because am×bm = (ab)m)
= 1/(2×-7)3
= 1/(-14)3
Q3Written answer
Find the value of:
(i) (30+4-1)×22
(ii) (2-1×4-1)÷2 – 2
(iii) (1/2)-2+(1/3)-2+(1/4)-2
(iv) (3-1+4-1+5-1)0
(v) {(-2/3)-2}2
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Worked solution
(i)(30+4– 1)×22 = (1+(1/4))×22
= ((4+1)/4 )×22
= (5/4)×22
= (5/22)×22
= 5×2(2-2)
= 5×20
= 5×1 = 5
(ii)(2-1×4-1)÷2-2
= [(1/2)×(1/4)] ÷(1/4)
= (1/2×1/22 )÷ 1/4
= 1/23÷1/4
= (1/8)×(4)
= 1/2
(iii) (1/2)-2+(1/3)-2+(1/4)-2
= (2-1)-2+(3-1)-2+(4-1)-2
= 2(-1×-2)+3(-1×-2)+4(-1×-2)
= 22+32+42
= 4+9+16
=29
(iv) (3-1+4-1+5-1)0
= 1
(v) {(-2/3)-2}2 = (-2/3)-2×2
= (-2/3)-4
= (-3/2)4
= 81/16
Q4Written answer
Evaluate:
(i) (8-1×53)/2-4
(ii) (5-1×2-2)×6-1
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Worked solution
(i) (8-1×53)/2-4
=
= 2×125 = 250
(ii) (5-1×2-2)×6-1
= (1/10)×1/6
= 1/60
Q5Written answer
Find the value of m for which 5m ÷ 5-3 = 55
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Worked solution
5m ÷ 5-3 = 55
5(m-(-3) ) = 55
5m+3 =55
Comparing exponents on both sides, we get
m+3 = 5
m = 5-3
m = 2
Q6Written answer
Evaluate:
(i)
(ii)
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Worked solution
(i)
= 3-4
= -1
(ii)
=
=
=
= 512/125
Q7Written answer
Simplify the following:
(i)
(ii)
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Worked solution
(i)
=
=
(ii)
=
=
=
=
= 1×1×3125
= 3125