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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