Students can refer to and download RD Sharma Solutions for Class 8 Maths Exercise 2.1 Chapter 2, Powers from the links provided below.
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RD Sharma Solutions for Class 8 Maths Exercise 2.1 Chapter 2 Powers
Access Answers to RD Sharma Solutions for Class 8 Maths Exercise 2.1 Chapter 2 Powers
1. Express each of the following as a rational number of the form p/q, where p and q are integers and q ≠ 0:
(i) 2-3
(ii) (-4)-2
(iii) 1/(3)-2
(iv) (1/2)-5
(v) (2/3)-2
Solution:
(i) 2-3 = 1/23 = 1/2×2×2 = 1/8 (we know that a-n = 1/an)
(ii) (-4)-2 = 1/-42 = 1/-4×-4 = 1/16 (we know that a-n = 1/an)
(iii) 1/(3)-2 = 32 = 3×3 = 9 (we know that 1/a-n = an)
(iv) (1/2)-5 = 25 / 15 = 2×2×2×2×2 = 32 (we know that a-n = 1/an)
(v) (2/3)-2 = 32 / 22 = 3×3 / 2×2 = 9/4 (we know that a-n = 1/an)
2. Find the values of each of the following:
(i) 3-1 + 4-1
(ii) (30 + 4-1) × 22
(iii) (3-1 + 4-1 + 5-1)0
(iv) ((1/3)-1 – (1/4)-1)-1
Solution:
(i) 3-1 + 4-1
1/3 + 1/4 (we know that a-n = 1/an)
LCM of 3 and 4 is 12
(1×4 + 1×3)/12
(4+3)/12
7/12
(ii) (30 + 4-1) × 22
(1 + 1/4) × 4 (we know that a-n = 1/an, a0 = 1)
LCM of 1 and 4 is 4
(1×4 + 1×1)/4 × 4
(4+1)/4 × 4
5/4 × 4
5
(iii) (3-1 + 4-1 + 5-1)0
(We know that a0 = 1)
(3-1 + 4-1 + 5-1)0 = 1
(iv) ((1/3)-1 – (1/4)-1)-1
(31 – 41)-1 (we know that 1/a-n = an, a-n = 1/an)
(3-4)-1
(-1)-1
1/-1 = -1
3. Find the values of each of the following:
(i) (1/2)-1 + (1/3)-1 + (1/4)-1
(ii) (1/2)-2 + (1/3)-2 + (1/4)-2
(iii) (2-1 × 4-1) ÷ 2-2
(iv) (5-1 × 2-1) ÷ 6-1
Solution:
(i) (1/2)-1 + (1/3)-1 + (1/4)-1
21 + 31 + 41 (we know that 1/a-n = an)
2+3+4 = 9
(ii) (1/2)-2 + (1/3)-2 + (1/4)-2
22 + 32 + 42 (we know that 1/a-n = an)
2×2 + 3×3 + 4×4
4+9+16 = 29
(iii) (2-1 × 4-1) ÷ 2-2
(1/21 × 1/41) / (1/22) (we know that a-n = 1/an)
(1/2 × 1/4) × 4/1 (we know that 1/a ÷ 1/b = 1/a × b/1)
1/2
(iv) (5-1 × 2-1) ÷ 6-1
(1/51 × 1/21) / (1/61) (we know that a-n = 1/an)
(1/5 × 1/2) × 6/1 (we know that 1/a ÷ 1/b = 1/a × b/1)
3/5
4. Simplify:
(i) (4-1 × 3-1)2
(ii) (5-1 ÷ 6-1)3
(iii) (2-1 + 3-1)-1
(iv) (3-1 × 4-1)-1 × 5-1
Solution:
(i) (4-1 × 3-1)2 (we know that a-n = 1/an)
(1/4 × 1/3)2
(1/12)2
(1×1 / 12×12)
1/144
(ii) (5-1 ÷ 6-1)3
((1/5) / (1/6))3 (we know that a-n = 1/an)
((1/5) × 6)3 (we know that 1/a ÷ 1/b = 1/a × b/1)
(6/5)3
6×6×6 / 5×5×5
216/125
(iii) (2-1 + 3-1)-1
(1/2 + 1/3)-1 (we know that a-n = 1/an)
LCM of 2 and 3 is 6
((1×3 + 1×2)/6)-1
(5/6)-1
6/5
(iv) (3-1 × 4-1)-1 × 5-1
(1/3 × 1/4)-1 × 1/5 (we know that a-n = 1/an)
(1/12)-1 × 1/5
12/5
5. Simplify:
(i) (32 + 22) × (1/2)3
(ii) (32 – 22) × (2/3)-3
(iii) ((1/3)-3 – (1/2)-3) ÷ (1/4)-3
(iv) (22 + 32 – 42) ÷ (3/2)2
Solution:
(i) (32 + 22) × (1/2)3
(9 + 4) × 1/8 = 13/8
(ii) (32 – 22) × (2/3)-3
(9-4) × (3/2)3
5 × (27/8)
135/8
(iii) ((1/3)-3 – (1/2)-3) ÷ (1/4)-3
(33 – 23) ÷ 43 (we know that 1/a-n = an)
(27-8) ÷ 64
19 × 1/64 (we know that 1/a ÷ 1/b = 1/a × b/1)
19/64
(iv) (22 + 32 – 42) ÷ (3/2)2
(4 + 9 – 16) ÷ (9/4)
(-3) × 4/9 (we know that 1/a ÷ 1/b = 1/a × b/1)
-4/3
6. By what number should 5-1 be multiplied so that the product may be equal to (-7)-1?
Solution:
Let us consider a number x
So, 5-1 × x = (-7)-1
1/5 × x = 1/-7
x = (-1/7) / (1/5)
= (-1/7) × (5/1)
= -5/7
7. By what number should (1/2)-1 be multiplied so that the product may be equal to (-4/7)-1?
Solution:
Let us consider a number x
So, (1/2)-1 × x = (-4/7)-1
1/(1/2) × x = 1/(-4/7)
x = (-7/4) / (2/1)
= (-7/4) × (1/2)
= -7/8
8. By what number should (-15)-1 be divided so that the quotient may be equal to (-5)-1?
Solution:
Let us consider a number x
So, (-15)-1 ÷ x = (-5)-1
1/-15 × 1/x = 1/-5
1/x = (1×-15)/-5
1/x = 3
x = 1/3
RD Sharma Solutions for Class 8 Maths Exercise 2.1 Chapter 2 Powers
Download the free RD Sharma Solutions Chapter 2 in PDF format, which provide answers to all the questions. Class 8 Maths Chapter 2 Powers Exercise 2.1 is based on problems which include negative exponents. These solutions are prepared by experienced faculty in accordance with the CBSE syllabus for the 8th Standard. The exercise-wise solutions are explained in a simple and easily understandable language to help students excel in the annual exam.
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