# FRANK Solutions for Class 9 Maths Chapter 9 - Indices

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## Chapter 9 - Indices Exercise Ex. 9.1

Question 9(b)

Solve for x:

3 x 7x = 7 x 3x

Solution 9(b)

Question 9(c)

Solve for x:

2x + 3 + 2x + 1 = 320

Solution 9(c)

Question 1

Solution 1

Question 2(a)

Evaluate the following:

Solution 2(a)

Question 2(b)

Evaluate the following:

Solution 2(b)

Question 2(c)

Evaluate the following:

Solution 2(c)

Question 3(a)

Write each of the following in the simplest form:

(a3)5 x a4

Solution 3(a)

Question 3(b)

Write each of the following in the simplest form:

a2 x a3 ÷ a4

Solution 3(b)

Question 3(c)

Write each of the following in the simplest form:

Solution 3(c)

Question 3(d)

Write each of the following in the simplest form:

a-3 x a2 x a0

Solution 3(d)

Question 3(e)

Write each of the following in the simplest form:

(b-2 - a-2) ÷ (b-1 - a-1)

Solution 3(e)

Question 4

Solution 4

Question 5(a)

Simplify the following and express with positive index:

3p-2q3 ÷ 2p3q-2

Solution 5(a)

Question 5(b)

Simplify the following and express with positive index:

Solution 5(b)

Question 6

Solution 6

Question 7(a)

Simplify the following:

Solution 7(a)

Question 7(b)

Simplify the following:

Solution 7(b)

Question 7(c)

Simplify the following:

Solution 7(c)

Question 7(d)

Simplify the following:

Solution 7(d)

Question 7(e)

Simplify the following:

Solution 7(e)

Question 7(f)

Simplify the following:

Solution 7(f)

Question 7(g)

Simplify the following:

Solution 7(g)

Question 7(h)

Simplify the following:

xm +2n. x3m-8n÷ x5m- 60

Solution 7(h)

Question 7(i)

Simplify the following:

Solution 7(i)

Question 7(j)

Simplify the following:

Solution 7(j)

Question 8

Solution 8

Question 9(a)

Solve for x:

22x + 1 = 8

Solution 9(a)

Question 9(d)

Solve for x:

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

Solution 9(d)

Question 9(e)

Solve for x:

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

Solution 9(e)

Question 9(f)

Solve for x:

1 = px

Solution 9(f)

Question 9(g)

Solve for x:

P3 x p-2 = px

Solution 9(g)

Question 9(h)

Solve for x:

Solution 9(h)

Question 9(i)

Solve for x:

Solution 9(i)

Question 9(j)

Solve for x:

Solution 9(j)

Question 9(k)

Solve for x:

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

Solution 9(k)

Question 9(l)

Solve for x:

Solution 9(l)

Question 9(m)

Solve for x:

Solution 9(m)

Question 9(n)

Solve for x:

Solution 9(n)

Question 9(o)

Solve for x:

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

Solution 9(o)

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

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

Solution 16

Question 17

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

Solution 17

Question 18

Solution 18

Question 19

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

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22(a)

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

Solution 22(a)

Question 22(b)

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

Solution 22(b)

Question 23(a)

Prove the following:

Solution 23(a)

Question 23(b)

Prove the following:

Solution 23(b)

Question 23(c)

Prove the following:

Solution 23(c)

Question 23(d)

Prove the following:

Solution 23(d)

Question 23(e)

Prove the following:

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

Solution 23(e)

Question 23(f)

Prove the following:

Solution 23(f)

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