NCERT solutions for Mathematics [English] Class 7 chapter 11 - Exponents and Powers [Latest edition]

Find the value of 2⁶.

Find the value of 9³.

Find the value of 11².

Find the value of 5⁴.

Express the following in exponential form:

6 × 6 × 6 × 6

Express the following in exponential form:

t × t

Express the following in exponential form:

b × b × b × b

Express the following in exponential form:

5 × 5 × 7 × 7 × 7

Express the following in exponential form:

2 × 2 × a × a

Express the following in exponential form:

a × a × a × c × c × c × c × d

Express the following number using exponential notation:

512

Express the following number using exponential notation:

343

Express the following number using exponential notation:

729

Express the following number using exponential notation:

3125

Identify the greater number, wherever possible, in the following?

4³ or 3⁴

Identify the greater number, wherever possible, in the following?

5³ or 3⁵

Identify the greater number, wherever possible, in the following?

2⁸ or 8²

Identify the greater number, wherever possible, in the following?

100² or 2¹⁰⁰

Identify the greater number, wherever possible, in the following?

2¹⁰ or 10²

Express the following as product of powers of its prime factor:

648

Express the following as product of powers of its prime factor:

405

Express the following as product of powers of its prime factor:

540

Express the following as product of powers of its prime factor:

3,600

Simplify:

2 × 10³

Simplify:

7² × 2²

Simplify:

2³ × 5

Simplify:

3 × 4⁴

Simplify:

0 × 10² _­­­­

Simplify:

5² × 3³

Simplify:

2⁴ × 3²

Simplify:

3² × 10⁴

Simplify:

(−4)³

Simplify:

(-3) × (-2)³

Simplify:

(-3)² × (-5)²

Simplify:

(−2)³ × (−10)³

Compare the following numbers:

2.7 × 10¹²; 1.5 × 10⁸

Compare the following numbers:

4 × 10¹⁴; 3 × 10¹⁷

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

3² × 3⁴ × 3⁸

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

6¹⁵ ÷ 6¹⁰

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

a³ × a²

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

7^x × 7²

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

`(5^2)^3 ÷ 5^3`

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

2⁵ × 5⁵

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

a⁴ × b⁴ 

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

(3⁴)³

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

`(2^20 ÷ 2^15) xx 2^3`

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

8^t ÷ 8²

Simplify and express the following in exponential form:

`(2^3 xx 3^4 xx 4)/(3 xx 32)`

Simplify and express the following in exponential form:

((5²)³ × 5⁴) ÷ 5⁷

Simplify and express the following in exponential form:

25⁴ ÷ 5³

Simplify and express the following in exponential form:

`(3 xx 7^2 xx 11^8)/(21 xx 11^3)`

Simplify and express the following in exponential form:

`3^7/(3^4 xx 3^3)`

Simplify and express the following in exponential form:

2⁰ + 3⁰ + 4⁰

Simplify and express the following in exponential form:

2⁰ × 3⁰ × 4⁰

Simplify and express the following in exponential form:

(3⁰ + 2⁰) × 5⁰

Simplify and express the following in exponential form:

`(2^8 xxa^5)/(4^3 xx a^3)`

Simplify and express the following in exponential form:

`(a^5/a^3)xx a^8`

Simplify and express the following in exponential form:

`(4^5 xx a^8b^3)/(4^5 xx a^5b^2)`

Simplify and express the following in exponential form:

`(2^3 xx 2)^2`

Say true or false and justify your answer:

10 × 10¹¹ = 100¹¹

Say true or false and justify your answer:

2³ > 5²

Say true or false and justify your answer:

2³ × 3² = 6⁵

Say true or false and justify your answer:

3⁰ = (1000)⁰

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

108 × 192

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

270

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

729 × 64

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

768

Simplify:

`((2^5)^2 xx 7^3)/(8^3 xx 7)`

Simplify:

`(25 xx 5^2 xx t^8)/(10^3 xx t^4)`

Simplify:

`(3^5 xx 10^5 xx 25)/(5^7 xx 6^5)`

Write the following number in the expanded form:

279404

Write the following number in the expanded form:

3006194

Write the following number in the expanded form:

2806196

Write the following number in the expanded form:

120719

Write the following number in the expanded form:

20068

Find the number from the following expanded form:

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

Find the number from the following expanded form:

4 × 10⁵ + 5 × 10³ + 3 × 10² + 2 × 10⁰

Find the number from the following expanded form:

3 × 10⁴ + 7 × 10² + 5 × 10⁰

Find the number from the following expanded form:

9 × 10⁵ + 2 × 10² + 3 × 10¹

Express the following number in standard form:

5,00,00,000

Express the following number in standard form:

70,00,000

Express the following number in standard form:

3,18,65,00,000

Express the following number in standard form:

3,90,878

Express the following number in standard form:

39087.8

Express the following number in standard form:

3908.78

Express the number appearing in the following statement in standard form:

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

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

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

Express the number appearing in the following statement in standard form:

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

Express the number appearing in the following statement in standard form:

Diameter of the Sun is 1,400,000,000 m.

Express the number appearing in the following statement in standard form:

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

Express the number appearing in the following statement in standard form:

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

Express the number appearing in the following statement in standard form:

The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.

Express the number appearing in the following statement in standard form:

60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

Express the number appearing in the following statement in standard form:

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

Express the number appearing in the following statement in standard form:

The population of India was about 1,027,000,000 in March, 2001.