Class 9th Maths – RD Sharma Chapter 2 : Exponents of Real Numbers Exercise 2.2 Solutions (Step-by-Step Guide)

RD Sharma Chapter 2 : Exponents of Real Numbers Exercise 2.2 Solutions

1. Simplify : (16^-1/5)^5/2 Watch Solution
2. Simplify : 5√(32)^2 Watch Solution
3. Simplify : 3√(343)^-2 Watch Solution
4. Simplify : (0.001)^1/3 Watch Solution
5. Simplify : [5(8^1/3+27^1/3)^3] Watch Solution
6. Simplify : [√2/5]^2/[√2/5]^13 Watch Solution
7. Simplify : [5^-1×7^2/5^2×7^-4]^7/2×[5^-2×7^3/5^3×7^-5]^-5/2 Watch Solution
8. Simplify : 64^-1/3(64^1/3 – 64^2/3) Watch Solution
9. Simplify : (1^3 + 2^3 + 3^3)^1/2 Watch Solution
10. Show that : (x^{a-b})^{a+b} (x^{b-c})^{b+c} (x^{c-a})^{c+a} = 1 Watch Solution
11. Show that : (3^a/3^b)^{a+b} (3^b/3^c)^{b+c} (3^c/3^a)^{c+a} = 1 Watch Solution
12. If 27^x = 9/3^x,find x Watch Solution
13. Find the value of x in the following : 2^5x/2^x = 5√2^20 Watch Solution
14. Find the value of x in the following : (2^3)^4 = (2^2)^x Watch Solution
15. Find the value of x in the following : (2/5)^x (5/3)^2x = 125/27 Watch Solution
16. Find the value of x in the following : 5^{x-2} × 3^{2x-3} =135 Watch Solution
17. Find the values of x in the following : 2^x-7 × 5^x-4 = 1250 Watch Solution
18. Find the values of x in the following : (3√4)^{(2x+1)/2} = 1/32 Watch Solution
19. Find the values of x in the following : 5^{2x+3} = 1 Watch Solution
20. Find the values of x in the following : (13)^√x = 4^4 – 3^4 – 6 Watch Solution
21. Find the values of x in the following : (√3/5)^{x+1} = 125/27 Watch Solution
22. If x = 2^1/3 + 2^2/3, show that x^3 – 6x = 6 Watch Solution
23. Determine (8x)^x, if 9^{x+2} = 240 + 9^x Watch Solution
24. If 3^x+1= 9^x-2, find the value of 2^1+x Watch Solution
25. If 3^4x = (81)^-1 and 10^1/y = 0.0001, find the value of 2^1+x Watch Solution
26. If 5^3x = 125 and 10^y = 0.001 find x and y Watch Solution
27. Solve the following equation : 3^x+1 = 27 × 3^4 Watch Solution
28. Solve the following equation : 4^2x = (3√16)^{-6/y} = (√8)^2 Watch Solution
29. Solve the following equation : 3^x-1 × 5^2y-3 = 225 Watch Solution
30. Solve the following equation : 8^x+1 = 16^y+2 and (1/2)^3+x = (1/4)^3y Watch Solution
31. Solve the following equation : 4^x-1 × (0.5)^3-2x = (1/8)^x Watch Solution
32. Solve the following equation √a/b = (b/a)^1-2x, where a, b are distinct positive primes. Watch Solution
33. if 2^x × 3^y × 5^z = 2160, find x, y and z. Hence, compute the value of 2^x × 2^-y × 5^-z. Watch Solution
34. If 1176 = 2^a × 3^b × 7^c, find the values of a, b and c. Hence compute the value of 2^a × 3^b × 7^-c as fraction Watch Solution
35. Assuming that x, y, z are positive real numbers, simplify the following : (√x^-3)^5 Watch Solution
36. Assuming that x, y, z are positive real numbers, simplify the following : √x^3y^-2 Watch Solution
37. Assuming that x, y, z are positive real numbers, simplify the following : 5√243x^10y^5z^10 Watch Solution
38. Assuming that x, y, z are positive real numbers, simplify the following : (x^-4/y^-10)^5/4 Watch Solution
39. Assuming that x, y, z are positive real numbers, simplify the following : (√2/√3)^5(6/7)^2 Watch Solution
40. Prove that : (√3×5^-3/3√3-1√5)×6√3×5^6 = 3/5 Watch Solution
41. Prove that : 9^3/2 – 3×5^0 – (1/81)^-1/2 = 15 Watch Solution
42. Prove that : (1/4)^-2 – 3 × 8^2/3 × 4^0 + (9/16)^-1/2 = 16/3 Watch Solution
43. Prove that : (2^1/2 × 3^1/2 × 4^1/4/10^-1/5 × 5^3/5)/(3^4/3 × 5^-7/5/4^-3/5 × 6) = 10 Watch Solution
44. Prove that : √1/4 + (0.01)^-1/2 – (27)^2/3 = 3/2 Watch Solution
45. Prove that : (2^n + 2^n-1)/(2^n+1 – 2^n) = 3/2 Watch Solution
46. Prove that : (64/125)^-2/3 + 1/(256/625)^1/4 + (√25/3√64)^0 = 61/16 Watch Solution
47. Prove that : {(0.6)^0 – (0.1)^-1}/{(3/8)^-3 (3/2)^3 – (1/3)^-1} = -3/2 Watch Solution
48. Prove that : (3^-3 × 6^2 × √98)/(5^2 × 3√1/25 × (15)^-4/3 × 3^1/3) = 28√2 Watch Solution
49. If x, y, a, b are positive real numbers, prove that : 1/(1+x^{a-b}) + 1/(1+x^{b-a}) = 1 Watch Solution
50. If x, y, a, b are positive real numbers, prove that : [{x^a(a-b)/x^a(a+b)}/{x^b(b-a)/x^b(b+a)}]^a+b = 1 Watch Solution
51. If x, y, a, b are positive real numbers, prove that : (1/x^a-b)^1/a-c(1/x^-c)^1/b-a(1/x^c-a)^1/c-b = 1 Watch Solution
52. If x, y, a, b are positive real numbers, prove that : {(x^a-a^-1)^1/a-1}^a/a+1 = x Watch Solution
53. If x, y, a, b are positive real numbers prove that (a^x+1/a^y+1)^x+y (a^y+2/a^z+2)^y+z (a^z+3/a^x+3)^z+x = 1 Watch Solution
54. If x, y, a, b are positive real numbers prove that : (x^a^2+b^2/x6ab)^a+b) (x^b^2+c^2/x^bc)^b+c (x^c^2+a^2/x^ac)^a+c = x^2(a^3+b^3+c^3) Watch Solution
55. If 2^x = x^y = 12^z,show that 1/z = 1/y + 2/x Watch Solution
56. If 2^x = 3^y = 6^-z, show that 1/x + 1/y + 1/z = 0 Watch Solution
57. If a^x = b^y = c^z and b^2 = ac, then show that y = 2zx/(z + x) Watch Solution
58. If 3^x = 5^y = (75)^z, show that z = xy/(2x + y) Watch Solution
59. If a and b are distinct positive primes such that 3√a^6b^-4 = a^x b^2y, find x and y. Watch Solution
60. If a and b are different positive primes such that : (a^-1b^2/a^2b^-4)^7/(a^3b^-5/a^-2b^3) = a^xb^y, find x and y Watch Solution
61. If a and b are different positive primes such that : (a + b)^-1(a^-1 + b^-1) = a^x b^y, find x + y + 2. Watch Solution
62. Simplify : (x^a+b/x^c)^{a-b} (x^b+c/x6a)^{b-c} (x^c+a/x^b)^{c-a} Watch Solution
63. Simplify : lm√x^l/x^m × mn√x^m/x^n × nl√x^n/x^1 Watch Solution
64. Show that : [(a+1/b)^m × (a-1/b)^n]/[(b+1/a)^m × (b-1/a)^n] = (a/b)^{m+n} Watch Solution
65. if ax^m+n y^1, b = x^n+1 y^m and c = x^l+m y^n, prove that a^m-n b^n-l c^l-m = 1 Watch Solution
66. If x = a^m = n, y = a^n+1and z = a^l+m, prove that x^m y^n z^l = x^n y^l z^m Watch Solution

 

 

2. Exponents of Real Numbers – R.D. Sharma Class 9th Maths

1. Exponents of a Real Numbers Exercise 2.1 Video Solutions
2. Exponents of a Real Numbers Exercise 2.2 Video Solutions
3. Exponents of a Real Numbers Very Short Answer Questions (VSAQs) Video Solutions
4. Exponents of a Real Numbers Fill in the Blanks (FBQs) Video Solutions
5. Exponents of a Real Numbers Multiple Choice Questions (MCQs) Video Solutions