Chapter 9 : Indices - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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Chapter 9 - Indices Excercise Ex. 9.1

Question 1

Solve for x:

3 x 7x = 7 x 3x

Solution 1

  

Question 2

Solve for x:

2x + 3 + 2x + 1 = 320

Solution 2

  

Question 3

Solution 3

Question 4

Evaluate the following:

  

Solution 4

Question 5

Evaluate the following:

  

Solution 5

Question 6

Evaluate the following:

  

Solution 6

Question 7

Write each of the following in the simplest form:

(a3)5 x a4

Solution 7

Question 8

Write each of the following in the simplest form:

a2 x a3 ÷ a4

Solution 8

Question 9

Write each of the following in the simplest form:

  

Solution 9

Question 10

Write each of the following in the simplest form:

a-3 x a2 x a0

Solution 10

Question 11

Write each of the following in the simplest form:

(b-2 - a-2) ÷ (b-1 - a-1)

Solution 11

Question 12

Solution 12

Question 13

Simplify the following and express with positive index:

3p-2q3 ÷ 2p3q-2

Solution 13

Question 14

Simplify the following and express with positive index:

  

Solution 14

Question 15

Solution 15

Question 16

Simplify the following:

Solution 16

Question 17

Simplify the following:

  

Solution 17

Question 18

Simplify the following:

  

Solution 18

Question 19

Simplify the following:

  

Solution 19

Question 20

Simplify the following:

  

Solution 20

Question 21

Simplify the following:

  

Solution 21

Question 22

Simplify the following:

  

Solution 22

Question 23

Simplify the following:

xm +2n. x3m-8n÷ x5m- 60

Solution 23

Question 24

Simplify the following:

  

Solution 24

Question 25

Simplify the following:

  

Solution 25

Question 26

Solution 26

Question 27

Solve for x:

22x + 1 = 8

Solution 27

Question 28

Solve for x:

9 x 3x = (27)2x - 5

Solution 28

Question 29

Solve for x:

22x + 3 - 9 x 2x + 1 = 0

Solution 29

  

Question 30

Solve for x:

1 = px

Solution 30

Question 31

Solve for x:

P3 x p-2 = px

Solution 31

  

Question 32

Solve for x:

  

Solution 32

Question 33

Solve for x:

Solution 33

Question 34

Solve for x:

  

Solution 34

Question 35

Solve for x:

22x- 1 -9 x 2x - 2 + 1= 0

Solution 35

  

Question 36

Solve for x:

Solution 36

Question 37

Solve for x:

  

Solution 37

Question 38

Solve for x:

  

Solution 38

Question 39

Solve for x:

9x + 4 = 32 x (27)x+1

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Find the value of (8p)p if 9p + 2 - 9p = 240.

Solution 46

Question 47

If ax = by = cz and abc = 1, show that

Solution 47

Question 48

Solution 48

Question 49

If 2250 = 2a. 3b. 5c, find a, b and c. Hence, calculate the value of 3a x 2-b x 5-c.

Solution 49

Question 50

Solution 50

Question 51

Solution 51

Question 52

Find the value of 'a' and 'b' if:

  

Solution 52

Question 53

Find the value of 'a' and 'b' if:

Solution 53

Question 54

Prove the following:

Solution 54

Question 55

Prove the following:

  

Solution 55

Question 56

Prove the following:

  

Solution 56

Question 57

Prove the following:

  

Solution 57

Question 58

Prove the following:

(xa)b-c x (xb)c-a x (xc)a-b = 1

Solution 58

Question 59

Prove the following:

Solution 59

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