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NCERT Solutions for Class 8 Maths Chapter 2 Power play - Exercise 2.1

Mastering the rules of indices is simple with our NCERT Solutions for Class 8 Maths Ch 2: Power Play Exercise 2.1. The title for this chapter is “Exponents and Powers”. In this chapter, we will learn how to use exponents as a mathematical shorthand to show repeated multiplication. Exercise 2.1 focuses on learning how to use negative exponents, evaluating powers with positive integers, and simplifying algebraic expressions by applying the basic laws of exponents.

Class 8 Math Lessons (Ch2): Learn to Work with Large and Small Numbers with Ease! The solutions to Exercise 2.1 of Class 8 Maths will be presented in a step-by-step approach so as to give students a good understanding of what you can do with $a^{- n} = 1/ a^{n}$ and also demonstrate how to use the product and quotient rules. The solutions are in accordance with the CBSE Guidelines so as to provide students with the best path available to improve their speed and accuracy in calculations. Additionally, these solutions will aid students in building a solid foundation for their future studies in Algebra and Scientific Notation.

1.0Download Class 8 Maths Chapter 2 Ex 2.1 NCERT Solutions PDF

You can get our simple NCERT Solutions for Class 8 Maths Chapter 2 Exercise 2.1 in PDF format. Ideal for rapid reference and offline study before tests.

NCERT Solutions Class 8 Maths Chapter 2 Ex 2.1

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2.0NCERT Solutions for Class 8 Maths Chapter 2 Power Play : All Exercises

NCERT Solutions for Class 8 Maths Chapter 2 Power Play - Exercise 2.1

NCERT Solutions for Class 8 Maths Chapter 2 Power Play - Exercise 2.2

3.0Detailed NCERT Class 8 Maths Chapter 2 Solutions of Exercise 2.1

1.Express the following in exponential form: (i) $6 \times 6 \times 6 \times 6$ (ii) $y \times y$ (iii) $b \times b \times b \times b$ (iv) $5 \times 5 \times 7 \times 7 \times 7$ (v) $2 \times 2 \times a \times a$ (vi) $a \times a \times a \times c \times c \times c \times c \times d$

Sol. (i) $6 \times 6 \times 6 \times 6 = 6^{4}$ (ii) $y \times y = y^{2}$ (iii) $b \times b \times b \times b = b^{4}$ (iv) $5 \times 5 \times 7 \times 7 \times 7 = 5^{2} \times 7^{3}$ (v) $2 \times 2 \times a \times a = 2^{2} \times a^{2}$ (vi) $a \times a \times a \times c \times c \times c \times c \times d$

2.Express each of the following as a product of powers of their prime factors in exponential form. (i) 648 (ii) 405 (iii) 540 (iv) 3600

Sol. (i) Prime factors of 648 $= 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3$ Exponential form of $648 = 2^{3} \times 3^{4}$ (ii) Prime factors of 405 $= 3 \times 3 \times 3 \times 3 \times 5$ Exponential form of 405=34 × 5 (iii) Prime factors of 540 $= 2 \times 2 \times 3 \times 3 \times 3 \times 5$ Exponential form of 540 $= 2^{2} \times 3^{3} \times 5$ (iv) Prime factors of 3600

$= 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5$

Exponential form of 3600 $= 2^{4} \times 3^{2} \times 5^{2}$ 3. Write the numerical value of each of the following: (i) $2 \times 1 0^{3}$ (ii) $7^{2} \times 2^{3}$ (iii) $3 \times 4^{4}$ (iv) $(- 3)^{2} \times (- 5)^{2}$ (v) $3^{2} \times 1 0^{4}$ (vi) $(- 2)^{5} \times (- 10)^{6}$

Sol. (i) $2 \times 1 0^{3} = 2 \times 10 \times 10 \times 10$

$= 2 \times 1000 = 2000$

(ii) $7^{2} \times 2^{3} = 7 \times 7 \times 2 \times 2 \times 2$

$= 49 \times 8 = 392$

(iii) $3 \times 4^{4} = 3 \times 4 \times 4 \times 4 \times 4$

$= 3 \times 256 = 768$

(iv) $(- 3)^{2} \times (- 5)^{2} = - 3 \times - 3 \times - 5 \times - 5$

$= 9 \times 25 = 225$

Negative numbers raised to even powers become positive. (v) $3^{2} \times 1 0^{4} = 3 \times 3 \times 10 \times 10 \times 10 \times 10$

$= 9 \times 10, 000 = 90, 000$

(vi) $(- 2)^{5} \times (- 10)^{6}$

$= = = (- 2) \times (- 2) \times (- 2) \times (- 2) \times (- 2) \times (- 10) \times (- 10) \times (- 10) \times (- 10) \times (- 10) \times (- 10) (- 32) \times (10, 00, 000) - 3, 20, 00, 000$

Odd power of a negative number remains negative, even power becomes positive.

Multiple choice questions

1.Which expression is not equivalent to $3 \times 3 \times 3 \times 3 \times 3 \times 3$ (1) $3^{6}$ (2) 18 (3) $9^{3}$ (4) 729

2. If $m$ is a positive integer, which of the following is not equal to $(2^{4})^{m}$ ? (1) 24 m (2) $4^{2 m}$ (3) $2^{m} (2^{3 m})$ (4) $4^{m} (2^{m})$

3. Which expression is equivalent to 81 ? (1) $2^{9}$ (2) $(\frac{1}{3})^{- 4}$ (3) $3^{- 5}$ (4) $(\frac{1}{3})^{4}$

4. The reciprocal of $(\frac{1}{3})^{- 2}$ is (1) 9 (2) $\frac{1}{9}$ (3) $\frac{1}{4}$ (4) None of these

5. The value of $(6^{- 1} - 7^{- 1})^{- 1} - (5^{- 1} - 4^{- 1})^{- 1}$ is equal to (1) $\frac{1}{2}$ (2) $\frac{1}{3}$ (3) $\frac{1}{4}$ (4) None of these

6. $[3^{3} + 3^{2} + 3^{- 2} + 3^{- 3}]$ is equal to (1) 0 (2) $36 + \frac{1}{36}$ (3) $\frac{976}{27}$ (4) $3^{5} + 3^{5}$

7. ${(\frac{5}{3})^{15}}^{0}$ is equal to (1) $\frac{5}{3}$ (2) $\frac{3}{5}$ (3) 1 (4) None of these

8. The value of $(\frac{5}{3})^{- 8} \div (\frac{5}{3})^{- 8}$ is equal to (1) $\frac{5}{3}$ (2) $\frac{3}{5}$ (3) 1 (4) None of these

9. $(\frac{a ^{- 1} b ^{2}}{a ^{2} b ^{- 4}})^{7} \div (\frac{a ^{3} b ^{- 5}}{a ^{- 2} b ^{3}})^{- 5}$ is equal to (1) $a^{4} b^{2}$ (2) $a^{2} b^{4}$ (3) $a^{3} b^{2}$ (4) $a^{2} b^{3}$

10. If $a = 36$ , then find the value of $a^{1/2} - a^{0}$ . (1) 36 (2) 6 (3) 1 (4) 5

11. Evaluate : $\frac{( 3 ^{4} ) ^{4} \times 9 ^{6}}{( 27 ) ^{7} \times 3 ^{9}}$ (1) 3 (2) 9 (3) $\frac{1}{3}$ (4) $\frac{1}{9}$

12. $[1 - 2 (1 - 2)^{- 1}]^{- 1}$ equals (1) $\frac{1}{3}$ (2) $- \frac{1}{3}$ (3) -1 (4) $\frac{1}{2}$

13. $[3^{2^{3}} - (3^{2})^{3}]$ is equal to (1) 8532 (2) 5832 (3) 3852 (4) 5238

14. The airports in the United States serve more than $635, 000, 000$ people each year. Which of the following is the same number written in scientific notation? (1) $635 \times 1 0^{6}$ (2) $6.35 \times 1 0^{8}$ (3) $6.35 \times 1 0^{- 8}$ (4) $6.35 \times 1 0^{9}$

15. The population of India is close to $1.08 \times 1 0^{9}$ . Which of the following represents this population written in standard notation? (1) $1, 080, 000, 000$ (2) $1, 080, 000$ (3) $180, 000, 000$ (4) 108,000

16. Ria has 5 skirts and 4 tops. She wants to wear one skirt and one top each day. How many different outfit combinations can she make? (1) 9 (2) 20 (3) 25 (4) 12

17. A school computer requires a 4-digit PIN for login. Each digit can be from 0 to 9 .

How many different PINs are possible? (1) 10,000 (2) 4,000 (3) 9,999 (4) 1,000

18. In a city, a vehicle number plate is made up of 2 letters (A-Z) followed by 2 digits (0-9).

How many unique number plates can be formed? (1) $26 \times 26 \times 10 \times 10 = 67, 600$ (2) $26 \times 10 \times 10 = 2, 600$ (3) $26 \times 26 \times 26 \times 10 = 175, 760$ (4) $10 \times 10 \times 10 \times 10 = 10, 000$

19. Statement-1: If 1 year $\approx 3.17 \times 1 0^{7}$ seconds then 15 million years in scientific notation is approximately equal to $4.8 \times 1 0^{14}$ seconds.

Statement-2: If 1 year $\approx 3.17 \times 1 0^{7}$ seconds then 15 million years in scientific notation is approximately equal to $4.8 \times 1 0^{15}$ seconds. (1) Statement-1 is true and statement-2 is false. (2) Statement-1 is false and statement-2 is true. (3) Both the statements are true. (4) Both the statements are false.

20. Statement-1: If 1 second $\approx 3.17 \times 1 0^{- 8}$ years then $1.5 \times 1 0^{16}$ seconds is approximately equal to around 495 million years.

Statement-2: If 1 second $\approx 3.17 \times 1 0^{- 8}$ years then $1.5 \times 1 0^{16}$ seconds is approximately equal to around 475 million years. (1) Statement-1 is true and statement-2 is false. (2) Statement-1 is false and statement-2 is true. (3) Both the statements are true. (4) Both the statements are false.

True or false

21. $(\frac{- 4}{5})^{4} \times (\frac{- 4}{5})^{2} = \frac{16}{25}$

22. $(\frac{2}{3})^{4} \div (\frac{2}{3})^{6} = (\frac{2}{3})^{2}$

23. $(\frac{1}{3})^{7 - 7} = 2^{0}$

24. $(\frac{- 7}{9})^{2} \div \frac{49}{81} = - 1$

Fill in the Blanks

25. $a^{m} \times a^{n} = a -$

26. The reciprocal of $a^{m}$ is $____$

27. $(2^{3})^{2} =$ $____$

28. Any non-zero number raised to the power 0 is equal to $____$ .

Crossword puzzle 29. Across b. If a number is squared, that tells you to multiply the number by itself $____$ times. g. If a number is cubed, it tells you to multiply the number by itself $____$ times. h. If you see a 3 with a little 4 above it you would say it is three to the $____$ power. i. What is another way to say to the third power? j. What is anything to the zero power? k. What do you multiply the bottom number by as many times as the exponent says?

Down

a. Five cubed could also be written five to the fifth $____$ c. What is another way to say to the second power? d. Even though they have special names, squares and cubes are still $____$ . e. What is zero to any power? f. Three to the eighth power would be $3 \times 3 \times 3 \times \dots$ how many times?

What exponent would you use for $4 \times 4 \times 4 \times 4 \times 4 ?$

Puzzle

30.Fill each cell so that each row and column multiplies to the given expression in the row and column. Note that each cell must be different. For example, if you use 'a' in one cell, you cannot use just 'a' in another cell. You could use '2a' or ' $a^{2}$ ', but not just an 'a'.

			$a^{2} b^{2}$
			$a b^{2} c^{3}$
			$2 a^{2} b^{2} c$
$a^{3} b^{2} c$	$2 a b^{3}$	$ab c^{3}$	$\times$

ANSWER KEY

Multiple choice questions

Question	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Answer	$2$	$4$	$2$	$2$	$4$	$3$	$3$	$3$	$1$	$4$	$4$	$1$	$2$	$2$	$1$
Question	16	17	18	19	20
Answer	$2$	$1$	$1$	$1$	$2$

True or false

21. False

22. False

23. True 2

4. False

Fill in the Blanks 25. $m + n$

26. a–m

27. 64

28. 1

Crossword puzzle

29.

Puzzle 30. Row1: $a, ab, b$

Row2: $c, b^{2}, c^{2} a$ Row3: $a^{2} b^{2}, 2, c$

4.0Key Concepts of Chapter 2 Power Play Exercise 2.1

Negative Exponents: Learning how to convert a negative power into a positive one by taking the reciprocal of the base.
Product Law: Adding exponents when multiplying powers with the same base.
Quotient Law: Subtracting exponents when dividing powers with the same base.
Power of a Power: Multiplying the internal and external exponents.
Zero Exponent: Understanding that any non-zero number raised to the power of zero equals one.
Evaluating Expressions Questions that require finding the final numerical value of terms with negative and positive integer exponents.
Simplification using Laws Applying the laws of exponents to condense complex expressions into a single power notation.
Finding Unknown Exponents Solving equations where a variable is placed in the exponent position by equating the bases on both sides.

5.0Benefits of NCERT Solutions for Class 8 Maths Chapter 2 Power Play Exercise 2.1

Conceptual Clarity: Detailed explanations of how negative exponents function.
Exam-Oriented: Covers all major question types found in CBSE school tests.
Logical Steps: Every solution is broken down to show which law is being applied at each stage.
Error Prevention: Highlights the difference between negative bases and negative exponents.

NCERT Class 8 Maths Ch. 2 Power Play Other Exercises:-

Exercise 2.1

Exercise 2.2