FRANK Solutions for Class 9 Maths Chapter 9 - Indices

FRANK Solutions for Class 9 Maths Chapter 9 - Indices

Chapter 9 - Indices Exercise Ex. 9.1

Question 1

Solve for x:

3 x 7^x = 7 x 3^x

Solution 1

 

Question 2

Evaluate the following:

 

Solution 2

Question 3

Solve for x:

2^{x + 3} + 2^{x + 1} = 320

Solution 3

 

Question 4

Evaluate the following:

 

Solution 4

Question 5

Evaluate the following:

 

Solution 5

Question 6

Write each of the following in the simplest form:

(a³)⁵ x a⁴

Solution 6

Question 7

Write each of the following in the simplest form:

a² x a³ ÷ a⁴

Solution 7

Question 8

Write each of the following in the simplest form:

 

Solution 8

Question 9

Write each of the following in the simplest form:

a^-3 x a² x a⁰

Solution 9

Question 10

Write each of the following in the simplest form:

(b^-2 - a^-2) ÷ (b^-1 - a^-1)

Solution 10

Question 11

Simplify the following and express with positive index:

3p^-2q³ ÷ 2p³q^-2

Solution 11

Question 12

Simplify the following and express with positive index:

 

Solution 12

Question 13

Simplify the following:

Solution 13

Question 14

Simplify the following:

 

Solution 14

Question 15

Simplify the following:

 

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:

x^{m +2n}. x^3m-8n÷ x^{5m- 60}

Solution 20

Question 21

Simplify the following:

 

Solution 21

Question 22

Simplify the following:

 

Solution 22

Question 23

Solve for x:

2^{2x + 1} = 8

Solution 23

Question 24

Solve for x:

9 x 3^x = (27)^{2x - 5}

Solution 24

Question 25

Solve for x:

2^{2x + 3} - 9 x 2^x + 1 = 0

Solution 25

 

Question 26

Solve for x:

1 = p^x

Solution 26

Question 27

Solve for x:

P³ x p^-2 = p^x

Solution 27

 

Question 28

Solve for x:

 

Solution 28

Question 29

Solve for x:

Solution 29

Question 30

Solve for x:

 

Solution 30

Question 31

Solve for x:

2^{2x- 1} -9 x 2^{x - 2} + 1= 0

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:

9^{x + 4} = 3² x (27)^x+1

Solution 35

Question 36

Solution 36

Question 37

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

Solution 37

Question 38

If a^x = b^y = c^z and abc = 1, show that

Solution 38

Question 39

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

Solution 39

Question 40

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

 

Solution 40

Question 41

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

Solution 41

Question 42

Prove the following:

Solution 42

Question 43

Prove the following:

 

Solution 43

Question 44

Prove the following:

 

Solution 44

Question 45

Prove the following:

 

Solution 45

Question 46

Prove the following:

(x^a)^b-c x (x^b)^c-a x (x^c)^a-b = 1

Solution 46

Question 47

Prove the following:

Solution 47

Question 48

Solution 48

Question 49

Solution 49

Question 50

Solution 50

Question 51

Solution 51

Question 52

Solution 52

Question 53

Solution 53

Question 54

Solution 54

Question 55

Solution 55

Question 56

Solution 56

Question 57

Solution 57

Question 58

Solution 58

Question 59

Solution 59