ICSE Class 9 Maths Selina Solutions Chapter 7 Indices (Exponents)

ICSE Class 9 Maths Selina Solution Chapter 7: The ICSE Class 9 Maths Selina Solution Chapter 7 is useful for students because it helps them to get high marks in the exam. Selina Solutions contains a detailed step-by-step explanation of all the problems in Chapter 7 Indices [Exponents] of Selina's Class 9 Notebook. To score well in the ICSE Class 9 Maths exam, it is recommended to solve the questions and for your betterment, we have provided the ICSE Class 9 Maths Selina Solutions Chapter 7 Indices (Exponents).

ICSE Class 9 Maths Selina Solutions Chapter 7

ICSE Class 9 Maths Selina Solutions Chapter 7 PDF

ICSE Class 9 Maths Selina Solutions Chapter 7 PDF

ICSE Class 9 Maths Selina Solutions Chapter 7 Indices (Exponents)

ICSE Class 9 Maths Selina Solutions Chapter 7 Exercise 7(A)

1. Evaluate:

(i) 3 ³ x (243) ^-2/3 x 9 ^-1/3

(ii) 5 ^-4 x (125) ^5/3 ÷ (25) ^-1/2

(iii) (27/125) ^2/3 x (9/25) ^-3/2

(iv) 7 ⁰ x (25) ^-3/2 – 5 ^-3

(v) (16/81) ^-3/4 x (49/9) ^3/2 ÷ (343/216) ^2/3

Solution:

2. Simplify:

(i) (8x ³ ÷ 125y ³ ) ^2/3

(ii) (a + b) ^-1 . (a ^-1 + b ^-1 )

(iii)

(iv) (3x ² ) ^-3 × (x ⁹ ) ^2/3

Solution:

3. Evaluate:

(i) √¼ + (0.01) ^-1/2 – (27) ^2/3

(ii) (27/8) ^2/3 – (1/4) ^-2 + 5 ⁰

Solution:

4. Simplify each of the following and express with positive index:

(i) (3 ^-4 /2 ^-8 ) ^1/4

(ii) (27 ^-3 /9 ^-3 ) ^1/5

(iii) (32) ^-2/5 ÷ (125) ^-2/3

(iv) [1 – {1 – (1 – n) ^-1 } ^-1 ] ^-1

Solution:

5. If 2160 = 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:

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

Solution:

7. Simplify:

(i)

(ii)

Solution:

8. Show that:

(a ^m /a ^-n ) ^m-n × (a ⁿ /a ^-l ) ^n-l × (a ^l /a ^-m ) ^l-m = 1

Solution:

9. If a = x ^m+n . x ^l ; b = x ^n+l . x ^m and c = x ^l+m . x ⁿ ,

Prove that: a ^m-n . b ^n-l . c ^l-m = 1

Solution:

10. Simplify:

(i)

(ii)

Solution:

(ii)

Exercise 7(B)

1. Solve for x:

(i) 2 ^2x+1 = 8

(ii) 2 ^5x-1 = 4 × 2 ^{3x + 1}

(iii) 3 ^{4x + 1} = (27) ^{x + 1}

(iv) (49) ^{x + 4} = 7 ² × (343) ^{x + 1}

Solution:

2. Find x, if:

(i) 4 ^2x = 1/32

(ii) √(2 ^x+3 ) = 16

(iii) [√(⅗)] ^x+1 = 125/27

(iv) [∛(⅔)] ^x-1 = 27/8

Solution:

3. Solve:

(i) 4 ^x-2 – 2 ^x+1 = 0

(ii)

Solution:

4. Solve:

(i) 8 × 2 ^2x + 4 × 2 ^x+1 = 1 + 2 ^x

(ii) 2 ^2x + 2 ^x+2 – 4 × 2 ³ = 0

(iii) (√3) ^x-3 = (∜3) ^x+1

Solution:

5. Find the values of m and n if:

4 ^2m = (∛16) ^-6/n = (√8) ²

Solution:

6. Solve x and y if:

(√32) ^x ÷ 2 ^y+1 = 1 and 8 ^y – 16 ^{4 – x/2} = 0

Solution:

7. Prove that:

(i) (x ^a /x ^b ) ^a+b-c . (x ^b /x ^c ) ^b+c-a . (x ^c /x ^a ) ^c+a-b = 1

(ii) x ^a(b-c) /x ^b(a-c) ÷ (x ^b /x ^a ) ^c = 1

Solution:

8. If a ^x = b, b ^y = c and c ^z = a, prove that: xyz = 1.

Solution:

9. If a ^x = b ^y = c ^z and b ² = ac, prove that: y = 2az/(x + z).

Solution:

10. If 5 ^-p = 4 ^-q = 20 ^r , show that: 1/p + 1/q + 1/r = 0.

Solution:

11. If m ≠ n and (m + n) ^-1 (m ^-1 + n ^-1 ) = m ^x n ^y , show that: x + y + 2 = 0

Solution:

12. If 5 ^{x + 1} = 25 ^{x – 2} , find the value of 3 ^{x – 3} × 2 ^{3 – x}

Solution:

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

Solution:

14. Solve for x:

(i) 4 ^x-1 × (0.5) ^{3 – 2x} = (1/8) ^-x

Solution:

(ii) (a ^{3x + 5} ) ² × (a ^x ) ⁴ = a ^{8x + 12}

Solution:

(iii) (81) ^3/4 – (1/32) ^-2/5 + x(1/2) ^-1 × 2 ⁰ = 27

Solution:

(iv) 2 ^{3x + 3} = 2 ^{3x + 1} + 48

Solution:

(v) 3(2 ^x + 1) – 2 ^x+2 + 5 = 0

Solution:

(vi) 9 ^x+2 = 720 + 9 ^x

Solution:

Exercise 7(C)

1. Evaluate:

(i) 9 ^5/2 – 3 x 8 ⁰ – (1/81) ^-1/2

(ii) (64) ^2/3 – ∛125 – 1/2 ^-5 + (27) ^-2/3 x (25/9) ^-1/2

(iii) [(-2/3) ^-2 ] ³ x (1/3) ^-4 x 3 ^-1 x 1/6

Solution:

2. Simplify:

Solution:

3. Solve: 3 ^x-1 × 5 ^2y-3 = 225.

Solution:

4. If [(a ^-1 b ² )/(a ² b ^-4 )] ⁷ ÷ [(a ³ b ^-5 )/(a ^-2 b ³ )] = a ^x .b ^y , find x + y.

Solution:

5. If 3 ^x+1 = 9 ^x-3 , find the value of 2 ^1+x .

Solution:

6. If 2 ^x = 4 ^y = 8 ^z and 1/2x + 1/4y + 1/8z = 4, find the value of x.

Solution:

7. If

Show that: m – n = 1

Solution:

8. Solve for x: (13) ^√x = 4 ⁴ – 3 ⁴ – 6.

Solution:

9. If 3 ^4x = (81) ^-1 and (10) ^1/y = 0.0001, find the value of 2 ^-x × 16 ^y .

Solution:

10. Solve: 3(2 ^x + 1) – 2 ^x+2 + 5 = 0.

Solution:

11. If (a ^m ) ⁿ = a ^m .a ⁿ , find the value of: m(n – 1) – (n – 1)

Solution:

12. If m = ∛15 and n = ∛14, find the value of m – n – 1/(m ² + mn + n ² )

Solution:

13. Evaluate:

Solution:

14. Evaluate:

(x ^q /x ^r ) ^1/qr × (x ^r /x ^p ) ^1/rp × (x ^p /x ^q ) ^1/pq

Solution:

15. (i) Prove that: a ^-1 /(a ^-1 + b ^-1 ) + a ^-1 /(a ^-1 – b ^-1 ) = 2b ² /(b ² – a ² )

Solution:

(ii) Prove that: (a + b + c)/(a ^-1 b ^-1 + b ^-1 c ^-1 + c ^-1 a ^-1 ) = abc

Solution:

16. Evaluate: 4/(216) ^-2/3 + 1/(256) ^-3/4 + 2/(243) ^-1/5

Solution:

Benefits of ICSE Class 9 Maths Selina Solutions Chapter 7 – Indices (Exponents)

1. Helps to plan a preparation strategy

2. Preparation Level Overview

3. Performance analysis

5. Time planning aids

6. Improve Accuracy and Speed ​​