Power Play — Hard

Q1. Consider two statements about the paper-folding situation. Statement I: After every fold, the thickness increases by a fixed amount, so it shows linear growth. Statement II: After every fold, the thickness is multiplied by 2, so it shows multiplicative (exponential) growth. Which is correct?

• A. Only Statement I is true.
• B. Only Statement II is true.
• C. Both statements are true.
• D. Neither statement is true.

Q2. After 46 folds the paper becomes thick enough to reach the Moon (≈ 3.84 × 10^5 km from Earth). Starting from thickness 0.001 cm, the thickness after 46 folds is best expressed as

• A. 0.001 cm × 46
• B. 0.001 cm × 2 × 46
• C. 0.001 cm × 46^2
• D. 0.001 cm × 2^46

Q3. Using the meaning of base and exponent the value of 7^2 × 2^3 is

• A. 98
• B. 196
• C. 392
• D. 14^6

Q4. Express 2 × 2 × a × a in exponential form. The correct form is

• A. 4a^2
• B. 2^2 × a^2
• C. (2a)^4
• D. 2^4 × a^4

Q5. Using the law n^a × n^b = n^(a + b) from, which of the following is NOT equal to 2^9?

• A. 2^4 × 2^5
• B. 2^6 × 2^3
• C. 2^7 × 2^2
• D. 2^4 × 2^3

Q6. Generalises (n^a)^b = n^(ab). Which one of the following rewritings of 2^10 is correct by this rule?

• A. (2^2)^5 = 2^10
• B. (2^3)^4 = 2^10
• C. (2^4)^4 = 2^10
• D. (2^5)^5 = 2^10

Q7. Using the quotient law 2^100 ÷ 2^25 in simplest exponential form equals

• A. 2^4
• B. 2^75
• C. 2^125
• D. 2^2500

Q8. Using the rule m^a × n^a = (mn)^a from, the value of 2^5 × 5^5 is

• A. 7^5
• B. 10^5
• C. 10^25
• D. 10^10

Q9. Simplify 2^(−4) × 2^7 using the laws of exponents from and 29. The value is

• A. 2^(−28)
• B. 2^11
• C. 2^3
• D. 2^(−3)

Q10. Simplify 3^2 × 3^(−5) × 3^6 using the product law extended to negative exponents . The answer is

• A. 3^(−60)
• B. 3^13
• C. 3^9
• D. 3^3

Q11. Looking at the 'Power Line of 4' Meera says: 'Going up the line, each step multiplies by 4. So 4^7 is 16 times bigger than 4^5.' Her statement is

• A. Correct, because 4^7 ÷ 4^5 = 4^2 = 16.
• B. Correct, because 7 − 5 = 2 and 4 × 2 = 8.
• C. Wrong, because 4^7 is 2 times bigger than 4^5.
• D. Wrong, because 4^7 is 4 times bigger than 4^5.

Q12. Extends the expanded form to decimals like 561.903 using powers of 10. The exponents used for the decimal digits 9, 0, 3 (in that order) are

• A. 10^1, 10^2, 10^3
• B. 10^(−1), 10^(−2), 10^(−3)
• C. 10^(−3), 10^(−2), 10^(−1)
• D. 10^0, 10^(−1), 10^(−2)

Q13. Writes large numbers in scientific (standard) form x × 10^y where 1 ≤ x < 10. The standard form of 20800 is

• A. 20.8 × 10^3
• B. 2.08 × 10^4
• C. 0.208 × 10^5
• D. 208 × 10^2

Q14. The Earth-Sun distance as 1.496 × 10^11 m and the Sun-Saturn distance as 1.4335 × 10^12 m. Roughly how many times farther is Saturn from the Sun than Earth is?

• A. About 0.1 times
• B. About 1 time (same distance)
• C. About 10 times
• D. About 100 times

Q15. A Class 8 student writes: '0.5 × 100 must be smaller than 100, because multiplication always makes a number bigger.' On the basis of of Ganita Prakash, the most useful teacher response is to

• A. Tell the student that multiplication and division are opposite, so the rule does not always apply.
• B. Show that multiplying by a number greater than 1 makes a number bigger, but multiplying by a number between 0 and 1 makes it smaller.
• C. Ask the student to memorise that 0.5 × 100 = 50 without explanation.
• D. Say that the rule is correct for whole numbers and stop the discussion there.