  ICSE Class 9 Indices Solution New Pattern

## ICSE Class 9 Indices Solution New Pattern By Clarify Knowledge

ICSE Class 9 Indices Solution New Pattern 2022

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

Question 1

Evaluate:

(i) (ii) (iii) (iv) (v) Solution 1

(i)

(ii)

(iii)

(iv)

(v)

Question 2

Simplify:

(i) (ii) (iii) (iv) Solution 2

(i)

(ii)

(iii)

(iv)

Question 3

Evaluate:

(i) (ii) Solution 3

(i)

(ii)

Question 4

Simplify each of the following and express with positive index:

(i) (ii) (iii) (iv) Solution 4

(i)

(ii)

(iii)

(iv)

Question 5

If 2160 = 2a. 3b. 5c, find a, b and c. Hence calculate the value of 3a 2-b 5-c.Solution 5

Question 6

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

Question 7

Simplify:

(i) (ii) Solution 7

(i)

(ii)

Question 8

Show that:

Solution 8

Question 9

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

Prove that: am - n. bn - l. cl - m = 1Solution 9

Question 10

Simplify:

(i) (ii) Solution 10

(i)

(ii)

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

Question 1

Solve for x:

(i) 22x+1 = 8

(ii) 25x-1 = 4 23x + 1

(iii) 34x + 1 = (27)x + 1

(iv) (49)x + 4 = 72 (343)x + 1Solution 1

(i)

(ii)

(iii)

(iv)

Question 2

Find x, if:

(i)

(ii)

(iii)

(iv) Solution 2

(i)

(ii)

(iii)

(iv)

Question 3

Solve:

(i) 4x - 2 - 2x + 1 = 0

(ii) Solution 3

(i)

(ii)

Question 4

Solve :

(i) 8 22x + 4 2x+1 = 1 + 2x

(ii)22x + 2x+2 - 4 23 = 0

(iii) Solution 4

(i)

(ii)

(iii)

Question 5

Find the values of m and n if:

Solution 5

Question 6

Solution 6

Question 7

Prove that:

(i) =1

(ii) Solution 7

(i)

(ii)

Question 8

If ax = b, by = c and cz = a, prove that: xyz = 1.Solution 8

Question 9

If ax = by = cz and b2 = ac, prove that : Solution 9

Question 10

If 5-P = 4-q = 20r, show that:

Solution 10

Question 11

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

x + y + 2 = 0Solution 11

Question 12

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

3x - 3 × 23 - xSolution 12

Question 13

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

Question 14 (i)

Solve for x:

4x-1 × (0.5)3 - 2x = Solution 14 (i)

Question 14 (ii)

Solve for x:

(a3x + 5)2. (ax)4 = a8x + 12Solution 14 (ii)

Question 14 (iii)

Solve for x:

Solution 14 (iii)

Question 14 (iv)

Solve for x:

23x + 3 = 23x + 1 + 48Solution 14 (iv)

Question 14 (v)

Solve for x:

3(2x + 1) - 2x + 2 + 5 = 0Solution 14 (v)

Question 14 (vi)

9x+2 = 720 + 9xSolution 14 (vi)

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

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

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solve: 3x-1× 52y-3 = 225.Solution 3

Question 4

Solution 4

Question 5

If 3x+1 = 9x-3, find the value of 21+x.Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solve: 3(2x + 1) - 2x+2 + 5 = 0.Solution 10

Question 11

If (am)n = am .an, find the value of:

m(n - 1) - (n - 1)Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15 (i)

Solution 15 (i)

Question 15 (ii)

Solution 15 (ii)

Question 16

Solution 16

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