R.D. Sharma Solutions Class 9th: Ch 2 Exponents of Real Numbers Exercise 2.2

Chapter 2 Exponents of Real Numbers R.D. Sharma Solutions for Class 9th Math Exercise 2.2

Exercise 2.2

1. Assuming that x, y, z are positive real numbers, simplify each of the following:

Solution

We have to simplify the following, assuming that x,y,z are positive real numbers.

2. Simplify

Solution

 3. Prove That

Solution 

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(ix)

4. Show that

Solution

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Level - 2

5.

Solution

6.

Solution

7.

Solution

8.

Solution

9.

Solution

10.  Find x in following

(iii) (3/5)^x(5/3)^x = 125/27

(iv) 5^x-2×3^2x-3 = 13

(v) 2^x-7×5^x-4 = 125/

(vii) 5^2x+3 = 1

Solution

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

11. If x = 2^1/3+3^2/3 show that x³ - 6x = 6

Solution

12. Determine (8x^x)^x, If 9^x+2 = 240 + 9^x

Solution

13. 3^x+1 = 9^x-2 Find the value of 2^1+x

Solution

14. If 3^4x = 81^-1 and 10^1/y = 0.0001, find the value of 2^-x+4y

Solution 

15. If 5^3x = 125, and 10^y = 0.001, find x and y.

Solution

16. Solve the following equations:

(i) 3^x+1 = 27×3⁴

Solution

Solution

18. If a and b are different positive primes such that

Solution

(i)

(ii)

19. If 2^x×3^y×5^z = 2160, find x, y and z. Hence, compute the value of 3^x×2^-y×5^-z

Solution

20. If 1176 = 2^a×3^b×7^c find a,b,c and compute 2^a×3^b×7^-c

Solution

21. Simplify

Solution

(i)

(ii)

22.  Show that

Solution

23.

(i)

Solution 

(i)

(ii)