RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions for Class 9 Mathematics

Created by: Abhishek Kapoor

Class 9 : RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

The document RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
All you need of Class 9 at this link: Class 9

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

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

2. Simplify

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

3. Prove that

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

4. Show that

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

Left hand side (LHS) = Right hand side (RHS)

Considering LHS,

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

Therefore, LHS = RHS

Hence proved

(ii)  RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

Left hand side (LHS) = Right hand side (RHS)

Considering LHS,

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

1

Therefore, LHS = RHS

Hence proved

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

5. If 2x = 3y = 12z ,  RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

6. If 2x = 3y = 6−z ,  RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev [by equating exponents]
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

 

  7. If ax = by = cz and b2 = ac , then show that  RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

8. If 3= 5= (75)z, show that 

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
We have,

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

3x = 2 − x       [On equating exponents]
3x + x = 2
4x = 2
x = 2/4
x = 12

Here the value of x is 1/2

10. Find the values of x in each of the following

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

We have

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

= 4x = 4    [On equatinge xponent]
x = 1

Hence the value of x is 1

(ii). (23)4 = (22)x

We have

(23)4 = (22)x

= 23×4 = 22×x

12 = 2x

2x = 12    [On equating exponents]

x = 6

Hence the value of x is 6

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

We have

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

x = 3     [on equating exponents]

Hence the value of x is 3

(iv) 5x−2×32x−3 = 135

We have,

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
⇒ x − 2 = 1,2x − 3 = 3       [On equating exponents]
⇒ x = 2 + 1,2x = 3 + 3
⇒ x = 3, 2x = 6 ⇒ x = 3

Hence the value of x is 3

(v). 2x−7×5x−4 = 1250

We have

2x−7×5x−4 = 1250

⇒ 2x−7×5x−4 = 2×625

⇒ 2x−7×5x−4 = 2×54

⇒ x−7 = 1 ⇒ x = 8,x−4 = 4 ⇒ x = 8

Hence the value of x is 8

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

4x+1 = −15

4x = −15−1

4x = −16

x =−16/4

x = −4

Hence the value of x is 4

(vii). 52x+3 = 1

52x+3 = 1×50

2x+3 = 0      [By equatinge xponents]

2x = −3

x = −3/2

Hence the value of x is −3/2

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev            [By equating exponents]
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
Hence the value of x is 4

RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-2.2, (Part - 1), Exponents Of Real Numbers, Class 9, Maths Class 9 Notes | EduRev

Hence the value of x is 7

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