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Class 8 Maths: Power Play (Exponents), 8 practice questions with answers

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These are 8 practice questions on Chapter 2, Power Play, of the new NCERT Class 8 Maths textbook, Ganita Prakash, Part 1. Each has a worked answer and the textbook page it comes from. They cover reading a square from prime-power exponents, spotting common mistakes with the laws of exponents for products, powers of powers and quotients, negative exponents, comparing powers with the same exponent, counting combinations with powers, correcting scientific notation, and how exponential growth races ahead of linear growth. Try each one on paper before you open the answer. The chapter before this one in the same book is A Square and A Cube.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 8, Part 1, Chapter 2, printed pages 19 to 46):

Writing and combining powers

Question 1. 7056 = 2⁴ × 3² × 7² and 7875 = 3² × 5³ × 7. Using only the exponents, explain why 7056 is a perfect square, write its square root as a product of prime powers, and say why 7875 is not a perfect square.

Answer: √7056 = 2² × 3 × 7 = 84; 7875 is not a square. A number is a perfect square when every prime appears an even number of times, because then the factors split into two equal halves. In 7056 the exponents 4, 2 and 2 are all even, so √7056 = 2² × 3¹ × 7¹ = 84 (halve each exponent). In 7875 the exponent of 5 is 3 and of 7 is 1, both odd, so it cannot be split into two equal halves and is not a perfect square. (Exponential form of a prime factorisation, page 22; power of a power, page 24.)

Question 2. Riya says 3⁵ × 3⁴ = 9⁹. Arun says 3⁵ × 3⁴ = 3²⁰. Both are wrong. Write the correct single power of 3, find its value, and explain each mistake.

Answer: 3⁹ = 19683. By nᵃ × nᵇ = nᵃ⁺ᵇ, 3⁵ × 3⁴ = 3⁵⁺⁴ = 3⁹ = 19683: there are 5 + 4 = 9 threes multiplied together. Riya multiplied the bases (3 × 3 = 9) as well as adding the exponents, but the base stays 3. Arun multiplied the exponents (5 × 4 = 20), which is the rule for a power of a power, (nᵃ)ᵇ, not for a product. (Product of powers and power of a power, page 24.)

Question 3. Is (5²)³ the same as 5²⁺³? Work out both and explain the difference.

Answer: no; (5²)³ = 5⁶ = 15625, but 5²⁺³ = 5⁵ = 3125. (5²)³ means 5² × 5² × 5², that is three groups of two 5s, so the exponents multiply: 5²ˣ³ = 5⁶ = 15625. 5²⁺³ is 5² × 5³, two 5s and then three more, so the exponents add: 5⁵ = 3125. A power of a power multiplies the exponents; a product of powers of the same base adds them. (Power of a power and product of powers, page 24.)

Question 4. Meena writes 6² ÷ 6⁵ = 6³. Ravi writes 6² ÷ 6⁵ = −6³. Who is right? Give the correct answer as a power of 6 and as a fraction.

Answer: neither; 6² ÷ 6⁵ = 6⁻³ = 1/216. By nᵃ ÷ nᵇ = nᵃ⁻ᵇ, 6² ÷ 6⁵ = 6²⁻⁵ = 6⁻³. Meena subtracted the wrong way round (5 − 2). Ravi treated a negative exponent as a negative number, but n⁻ᵃ = 1/nᵃ, so 6⁻³ = 1/6³ = 1/216, which is positive and smaller than 1. Check: (6 × 6) ÷ (6 × 6 × 6 × 6 × 6) leaves 1 on top and three 6s below. (Quotient of powers, page 27; negative exponents, pages 28 and 29.)

Question 5. Without working out the large numbers, decide which is larger: 7³ × 9³ or 61³. Explain.

Answer: 7³ × 9³ is larger. By mᵃ × nᵃ = (mn)ᵃ, 7³ × 9³ = (7 × 9)³ = 63³. Both numbers are now cubes, and 63 > 61, so 63³ > 61³. (Check: 63³ = 250047 and 61³ = 226981.) (Powers with the same exponent, page 25.)

Counting, large numbers and growth

Question 6. A quiz has 9 multiple-choice questions, each with 4 options, and a student marks one option for every question. In how many different ways can the answer sheet be filled?

Answer: 4⁹ = 262144 ways. Each of the 9 questions can be answered in 4 ways, and every choice for one question can go with every choice for the others, so the number of ways is 4 × 4 × … × 4 (9 times) = 4⁹ = 262144. (Counting combinations, pages 26 and 27.)

Question 7. Asha writes 6,74,00,000 = 67.4 × 10⁶ and 0.00083 = 0.83 × 10⁻³. Both values are correct, but neither is in scientific notation. Why not? Rewrite each correctly.

Answer: 6.74 × 10⁷ and 8.3 × 10⁻⁴. In scientific notation x × 10ʸ, the coefficient x must satisfy 1 ≤ x < 10. 67.4 is too big and 0.83 is too small. Moving the decimal point one place: 67.4 × 10⁶ = 6.74 × 10⁷, and 0.83 × 10⁻³ = 8.3 × 10⁻⁴ (making x ten times bigger makes the power of 10 one step smaller). (Scientific notation, page 31; negative exponents, pages 28 and 29.)

Question 8. A dish starts with 67 bacteria. In one experiment the number doubles every hour; in another, 67 more bacteria are added every hour. How many are there after 8 hours in each case?

Answer: 17152 by doubling; 603 by adding. Doubling for 8 hours multiplies the starting number by 2⁸: 67 × 2⁸ = 17152. Adding 67 each hour for 8 hours adds 67 × 8 = 536: 67 + 536 = 603. Doubling is exponential (multiplicative) growth, adding is linear (additive) growth and after only 8 hours the doubling dish already has far more bacteria. (Linear and exponential growth, pages 35 and 36.)

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 18.

The laws are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.