CG Board Class 9 Mathematics Chapter 3 Solutions: Exponent (घातांक) – 2026-27

There are four rice grains in one of the squares of a chessboard. In the second square next to it, the number of grains is four times of that, in the third square the number is four times of the second, and so on. Tell how many grains of rice will be there in the fourth square. Write it in exponent form.

Solve these

(i) 3⁵ × 3⁷

(ii) 17 × 17 × 17 × 17

(iii) 5 × 3 × 3 × 3 × 3

(iv) (2/3)³ × (2/3)⁵

(v) 2/5 × 2/5 × 2/5

Distance between Sun and Earth is approximately 150000000 km. Write it as an exponent.

Simplify the following

(i) (5⁴ × 5⁶)/(5³)

(ii) ((2²)³ × 8⁷)/(4⁴)

(iii) ((9 × 3)⁸)/(3⁵)

(iv) (3 × 2)⁴ × (2/3)⁶

Express the following numbers in exponent form

(i) 1/8

(ii) 1/243

(iii) 1/196

Write the multiplicative inverse of

(i) 10^-5

(ii) (1)/(2³)

(iii) P^-n

(iv) 5^-7

Simplify each of the following

(i) ((5²)³ × 5⁴) ÷ 5⁶

(ii) 2² × (3²)/(2^-2) × 3^-1

(iii) (14^-2 × 13^-2) ÷ 6^-1

Write the following numbers in expanded form of exponents

(i) 15.1

(ii) 512.23

(iii) 537.204

(iv) 205.003

Find the values of

(i) (16/81)^3/4 × (16/81)^5/4

(ii) (16/81)^{3/4 + 5/4}

(iii) (16/81)^{5/4 – 3/4}

(iv) 8^2/3

Which is the bigger number out of the pair?

(i) √(125), √36

(ii) √(121), √(729)

(iii) √(625), √(1024)

Write in descending order

Identify surd from √(3+√16), √(√16), √(2+√4) and write the reasons for your choice.

Write 3 numbers that are irrational but are not surds.

(i) (1/2)^-5**

(ii) (1/3)^-4

(iii) (2^-3 × 3^-7)/(6^-7)

(i) (-4)³ × (-2)^-3**

(ii) (-3)⁴ × (5/3)⁴

(iii) (-5)³ ÷ (5)^-7

(i) (16 × t^-3)/(4^-3 × 8 × t^-6) (t ≠ 0)**

(ii) {(1/3)^-1 – (1/4)^-1}^-1

(i) ((x^a)/(x^b))^a+b × ((x^b)/(x^c))^b+c × ((x^c)/(x^a))^c+a = 1**

(ii) (1)/(1 + x^m-n) + (1)/(1 + x^n-m) = 1

(i) 0.00000000000852

(ii) 8020000000000000

(iii) 41960000000

(i) 5.02 × 10^-6**

(ii) 7 × 10^-8

(iii) 1.00001 × 10⁹

(i) Size of red blood cells is 0.000007 m / :**

(ii) Diameter of Earth is 12756000 m / :

(iii) Thickness of a paper is 0.08 m / :

(i) (16)^1/2**

(ii) (243)^1/5

(iii) (15625)^1/6

(i) 23^1/2 × 23^3/2**

(ii) 11^4/3 × 11^5/3

(iii) 21^7/3 ÷ 21^1/3

(iv) 15^3/2 ÷ 15^5/2

(i) (625/81)^4/3 ÷ (625/81)^2/3**

(ii) (2/13)^4/3 ÷ (2/13)^5/3

(iii) 3 × 9^1/2 ÷ 9^3/2

(iv) 27^2/3 ÷ 27^1/3 × 27^4/3

(i) √81, √64, √(512)**

(ii) √(625), √(100), √(343)

(iii) √(216), √(243), √64

(iv) √(128), √(256), √(1000)

(i) √8**

• Analysis: 8 is a positive rational number and √8 = 2√2 is irrational.

*Surd.

(ii) √64

• Analysis: √64 = 4, which is rational.

*Not a surd.

(iii) √90

• Analysis: 90 is rational and √90 = 3√10 is irrational.

*Surd.

(iv) √(5+√2)

• Analysis: Radicand 5+√2 is irrational.

*Not a surd.

(v) √(2+√4)

• Analysis: √(2+2) = √4. Radicand 4 is rational and √4 is irrational.

*Surd.