SELINA Solutions for Class 9 Maths Chapter 7 - Indices (Exponents)

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 7 - Indices (Exponents) Exercise Ex. 7(A)

Question 1

Evaluate:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 1

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

 

(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 2

Simplify:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

Solution 2

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

 

 

Question 3

Evaluate:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

Solution 3

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

Question 4

Simplify each of the following and express with positive index:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 4

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 5

If 2160 = 2a. 3b. 5c, find a, b and c. Hence calculate the value of 3a Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents2-b Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents5-c.

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 6

If 1960 = 2a. 5b. 7c, calculate the value of 2-a. 7b. 5-c.

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

 

 

Question 7

Simplify:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents


(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 7

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 8

Show that:

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 9

If a = xm + n. yl; b = xn + l. . ym and c = xl + m. yn,

Prove that: am - n. bnl. cl - m = 1

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 10

Simplify:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 10

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Chapter 7 - Indices (Exponents) Exercise Ex. 7(B)

Question 1

Solve for x:

(i) 22x+1 = 8

(ii) 25x-1 = 4 Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents23x + 1

(iii) 34x + 1 = (27)x + 1

(iv) (49)x + 4 = 72Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents (343)x + 1

Solution 1

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 2

Find x, if:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 2

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents


(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 3

Solve:

(i) 4x - 2 - 2x + 1 = 0

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 3

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

Question 4

Solve :

(i) 8 Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents22x + 4Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 2x+1 = 1 + 2x

(ii)22x + 2x+2 - 4 Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents23 = 0

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 4

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 5

Find the values of m and n if:

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 6

 

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

 

Question 7

Prove that:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents=1

 

 (ii) Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 7

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 8

If ax = b, by = c and cz = a, prove that: xyz = 1.

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 9

If ax = by = cz and b2 = ac, prove that :Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents.

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 10

If 5-P = 4-q = 20r, show that:

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

 

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

 

Question 11

If m ≠ n and (m + n)-1 (m-1 + n-1) = mxny, show that:

 

 

x + y + 2 = 0

 

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

 

Question 12

If 5x + 1 = 25x - 2, find the value of

 

 

3x - 3 × 23 - x

 

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

 

Question 13

If 4x + 3 = 112 + 8 × 4x, find the value of (18x)3x.

 

 

 

 

Solution 13

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

 

Question 14

9x+2 = 720 + 9x

Solution 14

9x+2 = 720 + 9x

9x+2 - 9x = 720

9x (92 - 1) = 720

9x (81 - 1) = 720

9x (80) = 720

9x = 9

9x = 91

x = 1

Question 15

Solve for x:

 4x-1 × (0.5)3 - 2x = Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

  

 

 

 

 

Question 16

Solve for x:


(a3x + 5)2. (ax)4 = a8x + 12

 

Solution 16

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

 

Question 17

Solve for x:

 Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

 

Solution 17

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

 

Question 18

Solve for x:

23x + 3 = 23x + 1 + 48

 

Solution 18

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

 

 

 

Question 19

Solve for x:


3(2x + 1) - 2x + 2 + 5 = 0

 

Solution 19

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

 

Chapter 7 - Indices (Exponents) Exercise Ex. 7(C)

Question 1

Selina Solutions Icse Class 9 Mathematics Chapter - Indices ExponentsSelina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 1

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

Question 2

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

Question 3

Solve: 3x-1× 52y-3 = 225.

Solution 3

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 4

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

Question 5

If 3x+1 = 9x-3, find the value of 21+x.

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 6

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

Question 7

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

Question 8

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

Question 9

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

Question 10

Solve: 3(2x + 1) - 2x+2 + 5 = 0.

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 11

If (am)n = am .an, find the value of:

m(n - 1) - (n - 1)

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 12

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents 

Question 13

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 13

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 14

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 15

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 16

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 16

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Question 17

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

Solution 17

Selina Solutions Icse Class 9 Mathematics Chapter - Indices Exponents

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