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

[(–3)²]³ is equal to ______.

For a non-zero rational number x, x⁸ ÷ x² is equal to ______.

x is a non-zero rational number. Product of the square of x with the cube of x is equal to the ______.

For any two non-zero rational numbers x and y, x⁵ ÷ y⁵ is equal to ______.

a^m × aⁿ  is equal to ______.

(1⁰ + 2⁰ + 3⁰) is equal to ______.

The value of `(10^22 + 10^20)/10^20` is ______.

The standard form of the number 12345 is ______.

If 2¹⁹⁹⁸ – 2¹⁹⁹⁷ – 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = k.2¹⁹⁹⁵, then the value of k is ______.

Which of the following is equal to 1?

In standard form, the number 72105.4 is written as 7.21054 × 10ⁿ, where n is equal to ______.

Square of `(-2/3)` is ______.

The cube `((-1)/4)` is ______.

Which of the following is not equal to `((-5)/4)^4`?

Which of the following is not equal to 1?

`(2/3)^3 xx (5/7)^3` is equal to ______.

In standard form, the number 829030000 is written as K × 10⁸, where K is equal to ______.

Which of the following has the largest value?

1. 0.0001
2. `1/10000`
3. `1/10^6`
4. `1/10^6 ÷ 0.1`

In standard form 72 crore is written as ______.

For non-zero numbers a and b, `(a/b)^m ÷ (a/b)^n`, where m > n, is equal to ______.

Which of the following is not true?

Which power of 8 is equal to 2⁶?

`(-2)^31 xx (-2)^13 = (-2)^-`.

`(-3)^8 ÷ (-3)^5 = (-3)^-`.

`(11/15)^4 xx (_)^5 = (11/15)^9`

`((-1)/4)^3 xx ((-1)/4)^- = ((-1)/4)^11`

`[(7/11)^3]^4 = (7/11)^-`

`(6/13)^10 ÷ [(6/13)^5]^2 = (6/13)^-`

`[((-1)/4)^16]^2 = ((-1)/4)^-`

`(13/14)^5 ÷ (_)^2 = (13/14)^3`

`a^6 xx a^5 xx a^0 = a^-`

1 lakh = `10^-`.

1 million = `10^-`

729 = 3^—

432 = 2⁴ × 3^—

53700000 = ______ × 10⁷

88880000000 = ______ × 10¹⁰

27500000 = 2.75 × 10^—

340900000 = 3.409 × 10^—

Fill in the blanks with <, > or = sign

3² ______ 15

Fill in the blanks with <, > or = sign.

2³ ______ 3²

Fill in the blanks with <, > or = sign.

7⁴ ______ 5⁴

Fill in the blanks with <, > or = sign.

10,000 ______10⁵

Fill in the blanks with <, > or = sign.

6³ ______ 4⁴

One million = 10⁷

One hour = 60² seconds

1⁰ × 0¹ = 1

(–3)⁴ = –12

3⁴ > 4³

`((-3)/5)^100 = (-3^100)/(-5^100)`

(10 + 10)¹⁰ = 10¹⁰ + 10¹⁰

x⁰ × x⁰ = x⁰ ÷ x⁰ is true for all non-zero values of x.

In the standard form, a large number can be expressed as a decimal number between 0 and 1, multiplied by a power of 10.

4² is greater than 2⁴.

x^m + x^m = x^2m, where x is a non-zero rational number and m is a positive integer.

x^m × y^m = (x × y)^2m, where x and y are non-zero rational numbers and m is a positive integer.

x^m ÷ y^m = (x ÷ y)^m, where x and y are non-zero rational numbers and m is a positive integer.

x^m × xⁿ = x^m+n, where x is a non-zero rational number and m, n are positive integers.

4⁹ is greater than 16³.

`(2/5)^3 ÷ (5/2)^3` = 1

`(4/3)^5 xx (5/7)^5 = (4/3 + 5/7)^5`

`(5/8)^9 ÷ (5/8)^4 = (5/8)^4`

`(7/3)^2 xx (7/3)^5 = (7/3)^10`

5⁰ × 25⁰ × 125⁰ = (5⁰)⁶

876543 = 8 × 10⁵ + 7 × 10⁴ + 6 × 10³ + 5 × 10² + 4 × 10¹ + 3 × 10⁰

600060 = 6 × 10⁵ + 6 × 10²

4 × 10⁵ + 3 × 10⁴ + 2 × 10³ + 1 × 10⁰ = 432010

8 × 10⁶ + 2 × 10⁴ + 5 × 10² + 9 × 10⁰ = 8020509

4⁰ + 5⁰ + 6⁰ = (4 + 5 + 6)⁰

Arrange in ascending order:

2⁵, 3³, 2³ × 2, (3³)², 3⁵, 4⁰, 2³ × 3¹

Arrange in descending order:

2²⁺³, (2²)³, 2 × 2², `3^5/3^2`, 3^{2 ×} 3⁰, 2³ × 5²

By what number should (–4)⁵ be divided so that the quotient may be equal to (–4)³? 

Find m so that `(2/9)^3 xx (2/9)^6 = (2/9)^(2m - 1)`

If `p/q = (3/2)^2 ÷ (9/4)^0`, find the value of `(p/q)^3`.

Find the reciprocal of the rational number `(1/2)^2 ÷ (2/3)^3`

Find the value of:

7⁰

Find the value of:

7⁷ ÷ 7⁷

Find the value of:

`(–7)^(2 xx 7 - 6 - 8)`

Find the value of:

(2⁰ + 3⁰ + 4⁰) (4⁰ – 3⁰ – 2⁰)

Find the value of:

2 × 3 × 4 ÷ 2⁰ × 3⁰ × 4⁰

Find the value of:

(8⁰ – 2⁰) × (8⁰ + 2⁰)

Find the value of n, where n is an integer and 2^n–5 × 6^2n–4 = `1/(12^4 xx 2)`.

Express the following in usual form:

8.01 × 10⁷

Express the following in usual form:

1.75 × 10^–3

Find the value of 2⁵.

Find the value of (–3⁵).

Find the value of –(–4)⁴.

Express the following in exponential form:

3 × 3 × 3 × a × a × a × a

Express the following in exponential form:

a × a × b × b × b × c × c × c × c

Express the following in exponential form:

s × s × t × t × s × s × t

How many times of 30 must be added together to get a sum equal to 30⁷?

Express the following numbers using exponential notations:

1024

Express the following numbers using exponential notations:

1029

Express the following numbers using exponential notations:

`144/875`

Identify the greater number in the following:

2⁶ or 6²

Identify the greater number in the following:

2⁹ or 9²

Identify the greater number in the following: 

7.9 × 10⁴ or 5.28 × 10⁵

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

9000

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

2025

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

800

Express the following in single exponential form:

2³ × 3³

Express the following in single exponential form:

2⁴ × 4²

Express the following in single exponential form:

5² × 7²

Express the following in single exponential form:

(–5)⁵ × (–5)

Express the following in single exponential form:

(–3)³ × (–10)³

Express the following in single exponential form:

(–11)² × (–2)²

Express the following numbers in standard form:

76,47,000

Express the following numbers in standard form:

8,19,00,000

Express the following numbers in standard form:

5, 83,00,00,00,000

Express the following numbers in standard form:

24 billion

The speed of light in vaccum is 3 × 10⁸ m/s. Sunlight takes about 8 minutes to reach the earth. Express distance of Sun from Earth in standard form.

Simplify and express the following in exponential form:

`[(3/7)^4 xx (3/7)^5] ÷ (3/7)^7`

Simplify and express the following in exponential form:

`[(7/11)^5 ÷ (7/11)^2] xx (7/11)^2`

Simplify and express the following in exponential form:

(3⁷ ÷ 3⁵)⁴

Simplify and express the following in exponential form:

`(a^6/a^4) xx a^5 xx a^0`

Simplify and express the following in exponential form:

`[(3/5)^3 xx (3/5)^8] ÷ [(3/5)^2 xx (3/5)^4]`

Simplify and express the following in exponential form:

(5¹⁵ ÷ 5¹⁰) × 5⁵

Evaluate:

`(7^8 xx a^10b^7c^12)/(7^6 xx a^8b^4c^12)`

Evaluate:

`(5^4 xx 7^4 xx 2^7)/(8 xx 49 xx 5^3)`

Evaluate:

`(125 xx 5^2 xx a^7)/(10^3 xx a^4)`

Evaluate:

`(3^4 xx 12^3 xx 36)/(2^5 xx 6^3)`

Evaluate:

`((6 xx 10)/(2^2 xx 5^3))^2 xx 25/27`

Evaluate:

`(15^4 xx 18^3)/(3^3 xx 5^2 xx 12^2)`

Evaluate:

`(6^4 xx 9^2 xx 25^3)/(3^2 xx 4^2 xx 15^6)`

Express the given information in Scientific notation (standard form) and then arrange them in ascending order of their size.

Express the given information in Scientific notation and then arrange them in descending order of their size.

Write the number of seconds in scientific notation.

In our own planet Earth, 361,419,000 square kilometre of area is covered with water and 148,647,000 square kilometre of area is covered by land. Find the approximate ratio of area covered with water to area covered by land by converting these numbers into scientific notation.

If 2ⁿ⁺² – 2ⁿ⁺¹ + 2ⁿ = c × 2ⁿ, find the value of c.

A light year is the distance that light can travel in one year. 1 light year = 9,460,000,000,000 km.

1. Express one light year in scientific notation.
2. The average distance between Earth and Sun is 1.496 × 108 km. Is the distance between Earth and the Sun greater than, less than or equal to one light year?

The number of diagonals of an n-sided figure is `1/2(n^2 - 3n)`. Use the formula to find the number of diagonals for a 6-sided figure (hexagon).

Bacteria can divide in every 20 minutes. So 1 bacterium can multiply to 2 in 20 minutes. 4 in 40 minutes, and so on. How many bacteria will there be in 6 hours? Write your answer using exponents, and then evaluate.

Most bacteria reproduce by a type of simple cell division known as binary fission. Each species reproduce best at a specific temperature and moisture level.

Makes up 27 per cent of a blue whale’s body weight. Deepak found the average weight of blue whales and used it to calculate the average weight of their blubber. He wrote the amount as 22 × 32 × 5 × 17 kg. Evaluate this amount.

The major components of human blood are red blood cells, white blood cells, platelets and plasma. A typical red blood cell has a diameter of approximately 7 × 10^–6 metres. A typical platelet has a diameter of approximately 2.33 × 10^–6 metre. Which has a greater diameter, a red blood cell or a platelet?

A googol is the number 1 followed by 100 zeroes.

1. How is a googol written as a power?
2. How is a googol times a googol written as a power?

A student said that `3^5/9^5` is the same as `1/3`. What mistake has the student made?