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# Mathematics – Class 8 – Chapter 12 -Exponents and Powers- Exercise 12.1 – NCERT Exercise Solution

1. Evaluate:

(i) 3-2 (ii) (-4)-2 (iii) (1/2)-5

Solution:

(i) 3-2 = (1/3)2

[a-m = 1/am]

= 1/9

(ii) (-4)-2 = (1/-4)2

[a-m = 1/am]

= 1/16

(iii) (1/2)-5 = (2/1)5

[a-m = 1/am]

= 25

= 32

2. Simplify and express the result in power notation with positive exponent:

(i)(-4)5 ÷(-4)8

Solution:

= [ am / an = am-n]

= (-4)5-8

= 1/43

(ii) (1/23)2

Solution:

= 12/ (23)2

= 1/26

(iii) (-3)4× (5/3)4

Solution:

= (-3)4 × (54/34)

= 54

(iv) (3-7÷3-10) ×3-5

Solution:

= 3-7 – 10 × 3-5

= 33   × 3-5

= 3-2

= 1/32

(v) 2-3 × (-7)-3

Solution:

= [2× (-7)]-3

= (-14)-3

= -(1/143)

3. Find the value of:

(i)(30+4-1)×22

Solution:

= (1+(1/4)) ×22

= ((4+1)/4) ×22

= (5/4) ×4

= 5

(ii) (2-1×4-1) ÷2 – 2

Solution:

= [(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

Solution:

= (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

Solution:

= 1

(v) {(-2/3)-2}2

Solution:

= (-2/3)-2×2

= (-2/3)-4

= (-3/2)4

= 81/16

4. Evaluate

(i)(8-1×53)/2-4

(ii) (5-1×2-2) × 6-1

Solution:

5. Find the value of m for which 5m ÷ 5-3 = 55

Solution:

Given, 5m ÷ 5-3 = 55

5m-(-3) = 55 [am ÷ an = am-n]

5 m+3 = 55

Comparing the powers of equal bases

m + 3 = 5

m = 5 – 3 = 2

m = 2

6.Evaluate:

Solution:

Solution:

7. Simplify:

Solution:

Given:

Solution:

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