Solution of Chapter 13. Exponents and Powers (NCERT - Mathematics Book)

Find the value of:

(i) 2⁶

(ii) 9³

(iii) 11²

(iv) 5⁴

Express the following in exponential form:

(i) 6 × 6 × 6 × 6

(ii) t × t

(iii) b × b × b × b

(iv) 5 × 5 × 7 × 7 × 7

(v) 2 × 2 × a × a

(vi) a × a × c × c × c × c × d

Express each of the following numbers using exponential notation:

(i) 512

(ii) 343

(iii) 729

(iv) 3125

Identify the greater number, wherever possible, in each of the following.

(i) 4³ or 3⁴

(ii) 5³ or 3⁵

(iii) 2⁸ or 8²

(iv) 100² or 2¹⁰⁰

(v) 2¹⁰ or 10²

Express each of the following as product of powers of their prime factors:

(i) 648

(ii) 405

(iii) 540

(iv) 3600

Simplify:

(i) 2 × 10³

(ii) 7² × 2²

(iii) 2³ × 5

(iv) 3 × 4⁴

(v) 0 × 10²

(vi) 5² × 3³

(vii) 2⁴ × 3²

(viii) 3² × 10⁴

Simplify:

(i) (-4)³

(ii) (-3) × (-2)³

(iii) (-3)² × (-5)²

(iv) (-2)³ × (-10)³

Compare the following numbers:

(i) 2.7 × 10¹²; 1.5 × 10⁸

(ii) 4 × 10¹⁴; 3 × 10¹⁷

Using laws of exponents simplify and write the answer in exponential form:

(i) 3² × 3⁴ × 3⁸

(ii) 6¹⁵ 6¹⁰

(iii) a³ × a²

(iv) 7^x × 7²

(v) (5²)³ 5³

(vi) 2⁵ × 5⁵

(vii) a⁴ × b⁴

(viii) (3⁴)³

(ix) (2²⁰ 2¹⁵) × 2³

(x) (8^t 8²)

Simplify and express each of the following in exponential form:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

Say true or false and justify your answer:

(i) 10 × 10¹¹ = 100¹¹

(ii) 2³ > 5²

(iii) 2³ × 3² = 6⁵

(iv) 3⁰ = (1000)⁰

Express each of the following as a product of prime factors only in exponential form:

(i) 108 × 192

(ii) 270

(iii) 729 × 64

(iv) 768

Simplify:

(i)

(ii)

(iii)

Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

Find the number from each of the following expanded form:

(a) 8 × 10⁴ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰

(b) 4 × 10⁵ + 5 × 10³ + 3 × 10² + 2 × 10⁰

(c) 3 × 10⁴ + 7 × 10² + 5 × 10⁰

(d) 9 × 10⁵ + 2 × 10² + 3 × 10¹

Express the following numbers in standard form:

(i) 5, 00, 00, 000

(ii) 70, 00, 000

(iii) 3, 18, 65, 00, 000

(iv) 3, 90, 878

(v) 3, 9087.8

(vi) 3908.78

Express the number appearing in the following statements in standard form.

(a) The distance between Earth and Moon is 384,000,000 m.

(b) Speed of light in vacuum is 300,000,000 m/s.

(c) Diameter of the Earth is 1,27,56,000 m.

(d) Diameter of the Sun is 1,400,000,000 m.

(e) In a galaxy there are on an average 100,000,000,000 stars.

(f) The universe is estimated to be about 12,000,000,000 years old.

(g) The distance of the Sun form the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 gm.

(h) 60,230, 000,000,000,000,000,000 molecules are contained in a drop of water weighting 1.8 gm.

(i) The earth has 1,353,000,000 cubic km of sea water.

(j) The population of India was about 1,027,000,000 in March, 2001