NCERT Solution For Class 8 Math Chapter – 12 Exponents and Power Exercise – 12.1
Q1. Evaluate:
- 3-2
- (-4)-2
- (1/2)-5
Solution:-
- 3-2
= 1/9
- (-4)-2
= 1/16
- (1/2)-5
= 32
Q2. Simplify and express the result in power notation with positive exponent:
- (-4)4 / (-4)8
- (1/23)2
- -(3)4 x (5/3)4
- (3-7 / 3-10) x 3-5
- 2-3 x (-7)-3
Solution:-
- (-4)5 / (-4)8
= 1/(-4)3
- (1/23)2
= 1/23 x 2
= 1/26
- (-3)4 x (5/3)4
= 30 x 54 = 54
- (3-7 / 3-10) x 3-5
= 1/32
- 2-3 x (-7)-3
= 1(-14)3
Q3. Find the value of:
- (30 + 4-1) x 22
- (2-1 x 4-1) / 2-2
- (1/2)-2 + (1/3)-2 + (1/4)-2
- (3-1 + 4-1 + 5-1 )0
(V) {(-2/3)-2}2
Solution:-
(i)
= (1 +(1/4) x 22
= (4 + 1)/4) x 22
= (5/4) x 22
= (5/22) x 22
= 5 x 2 ( 2 – 2 )
= 5 x 1
= 5
(ii)
= [(1/2) x (1/4)] / (1/4)
= (1/8) x (4)
= 1/2
(iii)
= (2-1)-2 + (3-1)-2 + (4-1)-2
= 4 + 9 + 16
= 29
(iv)
= 1
(v)
= (-2/3)-4
= (-3/2)4
= 81/16
Q4. Evaluate
- (8-1 x 53)/2-4
- (5-1 x 2-2 ) x 6-1
Solution:-
(i)
= 2 x 1 25
= 250
(ii)
= (1/10) x 1/6
= 1/60
Q5. Find the value of m for which 5m / 5-3 = 55
Solution:-
5m / 5-3 = 55
5(m-(-3)) = 55
5m+3 = 55
M + 3 = 5
M = 5 – 3
M = 2
Q6. Evaluate
(i)
{ (1/3)-1 – (1/4)-1}-1
(ii)
(5/8)-7 x (8/5)-4
Solution:-
(i)
= { (3/1)1 – (4/1)1}
= 3 – 4
= -1
(ii)
= 5-7/8-7 x 8-4/5-4
= 5-7-(-4) x 8-4-(-7)
= 5/2/125
Q7. Simplify.
- 25 x t-4/ 5-3 x 10 x t-3 ( t ≠ 0)
- 3-5 x 10-5 x 125 / 5-7 x 6-5
Solution:-
(i)
= 52 x t-4/ 5-3 x 5 x 2 x t-8
625/2 t4
(ii)
= 3-5 x ( 2 x 5)-5 x 53 / 5-7 x (2 x 3)-5
= 1 x 3125 x 1
= 3125