Power Play — Mastery

Q1. Compares the paper-folding thickness after 26 folds (about 670 m) with the height of the Burj Khalifa (about 830 m). The closest correct comparison is

• A. After 26 folds the paper is taller than the Burj Khalifa.
• B. After 26 folds the paper is exactly half the Burj Khalifa.
• C. After 26 folds the paper is about ten times the Burj Khalifa.
• D. After 26 folds the paper is roughly the same height as the Burj Khalifa.

Q2. Damayanti compares two magical ponds Pond A doubles its lotuses each day and Pond B triples them. Both start with 1 lotus on day 1. After 5 days, by how many times is Pond B's count larger than Pond A's?

• A. About 16 times
• B. About 5 times
• C. About 1.5 times
• D. About 80 times

Q3. Using the rule that (−n)^a means (−n) multiplied by itself a times, the value of (−1)^5 is

• A. 5
• B. −5
• C. 1
• D. −1

Q4. From the meaning of an exponent , the value of 2 × 10^3 is

• A. 60
• B. 200
• C. 8000
• D. 2000

Q5. Apart from (4^3)^2, another power-of-a-power form for 4^6. Which one is also correct?

• A. (4^2)^3
• B. (4^6)^1 = (4^1)^6 only
• C. (4^2)^4
• D. (4^3)^3

Q6. On, the rule m^a × n^a = (mn)^a is stated in words. Choose the correct statement

• A. When two powers have the same exponent, multiplying them is the same as raising the product of the bases to that exponent.
• B. When two powers have the same base, multiplying them is the same as raising the sum of the exponents.
• C. When two powers have different bases, the larger base always wins.
• D. When two powers have the same exponent, divide the bases and raise to that exponent.

Q7. Generalises (n^a)^b for counting numbers a and b. The correct rule is (n^a)^b equals

• A. n^(a + b)
• B. n^(a − b)
• C. n^(a × b)
• D. (2n)^(a × b)

Q8. For any non-zero n, n^(−a) = 1/n^a. The value of 10^(−3) is

• A. −1000
• B. 1/30
• C. 1/1000
• D. −1/1000

Q9. On the 'Power Line of 4' , each step downward divides the previous value by 4. Starting from 4^2 = 16, what is the value two steps below — that is, at 4^0?

• A. 1
• B. 0
• C. 4
• D. 1/4

Q10. Write 172 in expanded form using powers of 10. The correct expanded form is

• A. (1 × 10^2) + (7 × 10^1) + (2 × 10^0)
• B. (1 × 10^3) + (7 × 10^2) + (2 × 10^1)
• C. (1 + 7 + 2) × 10^2
• D. 172 × 10^0

Q11. Four students write 65950 in scientific form. Using the rule x × 10^y with 1 ≤ x < 10 from, which writing is correct?

• A. Asha: 65.95 × 10^3
• B. Deep: 6595 × 10^1
• C. Chand: 0.6595 × 10^5
• D. Bina: 6.595 × 10^4

Q12. The population of Kohima as about 1.42 × 10^5. Written as an ordinary number (no powers of 10), this is approximately

• A. 14200
• B. 1420
• C. 142000
• D. 1420000

Q13. 'Tulābhāra' as a tradition in which a person is weighed against goods (jaggery, wheat, fruits) and the goods are then donated. According to the chapter, Tulābhāra is a tradition mainly found in

• A. Northern India
• B. Eastern India
• C. Southern India
• D. Western Himalayas

Q14. A Class 8 teacher wants children to feel why 10^7 is much larger than 10^4 — not just '3 more zeros'. Based of Ganita Prakash, the BEST first classroom activity is to

• A. Make children memorise that each extra zero multiplies the value by 10.
• B. Draw a 'Power Line of 10' on the board where each rightward step multiplies by 10, and have children walk from 10^4 to 10^7 step by step.
• C. Ask children to write the number 10^7 in their notebooks neatly.
• D. Give children a long list of population figures and ask them to copy them.

Q15. Estimates the number of water drops on Earth as 2 × 10^25 and the number of ants as 2 × 10^16. Roughly how many water drops are there for every ant?

• A. About 10^9
• B. About 10^16
• C. About 10^41
• D. About 10^25

Q16. On, Estu claims that a paper can be folded at most 7 times. Roxie disagrees and the chapter sets up the folding table to settle this. Which option BEST captures what the chapter shows about Estu's claim?

• A. Estu is right — after the 7th fold the paper is mathematically impossible to fold further.
• B. Estu is right because 2^7 = 128 is the largest power of 2 within paper-folding limits.
• C. Estu's claim is only a practical (physical) limit; mathematically the chapter folds the same paper 46 times to reach the Moon.
• D. Estu's claim refers to tripling, not doubling, so it is unrelated to 2^7.

Q17. Linear growth. Which of the following classroom situations is the BEST example of linear growth (not exponential)?

• A. A pond's lotuses double in number every day.
• B. A paper's thickness doubles after every fold.
• C. Savings of ₹50 are added to a piggy bank every week.
• D. Bacteria in a dish split into two every hour.

Q18. Using the fold-thickness pattern by how many times does the thickness of the paper increase after 3 folds from its original value?

• A. 3 times
• B. 6 times
• C. 8 times
• D. 9 times

Q19. The exponential expression n^3 means

• A. n + n + n
• B. n × n × n
• C. 3 × n
• D. n × 3 × 3

Q20. Asks to interpret a^3 × b^2. Written without exponents, this expression equals

• A. a × a × a × b × b
• B. a × b × a × b × a × b
• C. (a × b)^5
• D. 5 × a × b

Q21. Generalises the quotient law for exponents. For counting numbers a > b and any non-zero base n, n^a ÷ n^b equals

• A. n^(a + b)
• B. n^(a × b)
• C. n^(a − b)
• D. n^(a ÷ b)

Q22. Using the negative-exponent rule the value of 4^(−2) is

• A. −16
• B. 1/16
• C. −1/8
• D. 1/8

Q23. Using the negative-exponent rule which of the following is equal to 10^3?

• A. 10^(−3)
• B. 1/10^(−3)
• C. 1/10^3
• D. 10 × (−3)

Q24. Using the powers-of-10 method the population 80 lakh written in scientific (standard) form is

• A. 8 × 10^5
• B. 8 × 10^6
• C. 80 × 10^5
• D. 8 × 10^7

Q25. Writes 5-digit numbers in standard form x × 10^y with 1 ≤ x < 10. The standard form of 59853 is

• A. 59.853 × 10^3
• B. 5.9853 × 10^4
• C. 0.59853 × 10^5
• D. 5985.3 × 10^1

Q26. For a number in standard form x × 10^y (1 ≤ x < 10), the exponent y quickly tells the order of magnitude. Asha writes Kohima's population as 1.42 × 10^5 and Mumbai's as 2 × 10^7. Without computing, Mumbai's population is roughly

• A. 10 times Kohima's
• B. 100 times Kohima's
• C. 1000 times Kohima's
• D. 10000 times Kohima's

Q27. The world population of the northern white rhinoceros as 2 × 10^0. Written as an ordinary number, this means there are about

• A. 20 northern white rhinos in the world
• B. 2 northern white rhinos in the world
• C. 200 northern white rhinos in the world
• D. 0 northern white rhinos in the world

Q28. Before showing the table a teacher asks the class: 'Guess — after 30 folds of a 0.001 cm sheet, how thick will the paper be?' Most children guess between 3 cm and 30 cm. Based of Ganita Prakash, the BEST next teaching step is to

• A. Mark all answers wrong and write 10.7 km on the board.
• B. Make children list the thickness after each fold (0.001, 0.002, 0.004, …) and notice the doubling pattern before revealing the 30-fold value.
• C. Tell children the rule 0.001 × 2^n and ask them to apply it for n = 30 by calculator.
• D. Skip the guess and move on to exponential notation directly.

Q29. A Class 8 student writes 2^5 = 2 × 5 = 10. Based on the meaning of base and exponent which sequence of teaching steps best repairs this error?

• A. Mark it wrong, write 32 on the board, and move on.
• B. Read 2^5 aloud as 'two raised to the power 5', then show 2 × 2 × 2 × 2 × 2 = 32, then contrast with 2 × 5 = 10 on a separate line.
• C. Show 2^5 = 32 on a calculator and tell the student to remember it.
• D. Tell the student 2^5 just means 5 twos, without further explanation.

Q30. The African elephant population as 4 × 10^5 and the human population as 8.2 × 10^9. Roughly how many humans share the planet with each African elephant?

• A. About 20
• B. About 2050
• C. About 20500
• D. About 2 lakh