CBSE Class 8 Mathematics Power Play Very Short Answer Questions with Answers

Very Short Answer Questions

Question 1. Write 6 × 6 × 6 × 6 × 6 in exponential form.
Answer:
6 is multiplied by itself 5 times, so 6 × 6 × 6 × 6 × 6 = 6⁵.

Teacher's Note:
1. Count the factors to get the exponent.
2. The repeated number is the base.

Question 2. In the power 11⁴, name the base and the exponent.
Answer:
The base is 11 and the exponent (power) is 4; 11⁴ means 11 multiplied by itself 4 times.

Teacher's Note:
1. The base is written on the line, the exponent is raised.
2. Add the meaning to make the answer complete.

Question 3. Write the value of (−1)⁹ and state whether it is positive or negative.
Answer:
(−1)⁹ = −1, which is negative, because 9 negative factors leave one minus sign unpaired.

Teacher's Note:
1. Odd exponent on a negative base gives a negative answer.
2. Pair the minus signs to check.

Question 4. Find the value of 2⁶.
Answer:
2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64.

Teacher's Note:
1. Double step by step: 2, 4, 8, 16, 32, 64.
2. Do not compute 2 × 6.

Question 5. The thickness of a sheet of paper doubles with every fold. By what number is its original thickness multiplied after 5 folds?
Answer:
Each fold multiplies the thickness by 2, so after 5 folds it is multiplied by 2⁵ = 32.

Teacher's Note:
1. Doubling 5 times means multiplying by 2 five times.
2. This is multiplicative growth.

Question 6. What is the value of 17⁰?
Answer:
17⁰ = 1, since n⁰ = 1 for every non-zero number n.

Teacher's Note:
1. Any non-zero number to the power 0 is 1.
2. The answer is not 0 and not 17.

Question 7. Express 5⁻² as a fraction in its simplest form.
Answer:
5⁻² = \( \frac{1}{5^{2}} \) = \( \frac{1}{25} \).

Teacher's Note:
1. A negative exponent means the reciprocal.
2. The answer is positive.

Question 8. Write \( \frac{1}{10^{4}} \) using a negative exponent.
Answer:
\( \frac{1}{10^{4}} \) = 10⁻⁴, using the rule \( \frac{1}{n^{a}} \) = n^−a.

Teacher's Note:
1. Moving a power from the denominator to the top changes the sign of its exponent.
2. 10⁻⁴ = 0.0001.

Question 9. State the rule for dividing two powers that have the same non-zero base.
Answer:
For a non-zero base n, \( n^{a} \div n^{b} = n^{a-b} \); keep the base and subtract the exponents.

Teacher's Note:
1. The base must not be 0.
2. Subtract the exponent of the divisor.

Question 10. Write 1 crore as a power of 10.
Answer:
1 crore = 1,00,00,000 = 10⁷ (1 followed by 7 zeros).

Teacher's Note:
1. Count the zeros to get the exponent.
2. 1 lakh = 10⁵, 1 crore = 10⁷.

Question 11. Write 4.5 × 10⁴ in the usual form.
Answer:
4.5 × 10⁴ = 4.5 × 10000 = 45000.

Teacher's Note:
1. Move the decimal point 4 places to the right.
2. Fill empty places with zeros.

Question 12. Which number is called a googol? Write it as a power of 10.
Answer:
A googol is 1 followed by one hundred zeros, that is 10¹⁰⁰.

Teacher's Note:
1. The exponent equals the number of zeros.
2. A googol is larger than the number of atoms in the universe.

Question 13. Express 1080 as a product of powers of its prime factors.
Answer:
1080 = 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2³ × 3³ × 5.

Teacher's Note:
1. Divide by the smallest prime again and again.
2. Check: 8 × 27 × 5 = 1080.

Question 14. Simplify 7⁵ × 7⁻³ and write its numerical value.
Answer:
7⁵ × 7⁻³ = 7^{5 + (−3)} = 7² = 49.

Teacher's Note:
1. Add the exponents, keeping their signs.
2. The product law works for negative exponents too.

Question 15. Write 9¹⁰ as a power of a power in two different ways.
Answer:
9¹⁰ = (9²)⁵ and 9¹⁰ = (9⁵)², since (n^a)^b = n^ab and 2 × 5 = 5 × 2 = 10.

Teacher's Note:
1. Split the exponent 10 into two factors.
2. (9¹)¹⁰ is also correct but less interesting.

Question 16. A stall offers 3 kinds of bread, 4 kinds of filling and 2 kinds of sauce. In how many different ways can one sandwich be made?
Answer:
Each choice is made independently, so the number of sandwiches = 3 × 4 × 2 = 24.

Teacher's Note:
1. Independent choices are multiplied, not added.
2. This is the counting idea behind powers.

Question 17. Express 2,04,000 in standard form.
Answer:
2,04,000 = 2.04 × 10⁵, as the decimal point moves 5 places to the left and the coefficient lies between 1 and 10.

Teacher's Note:
1. Keep the zero in the middle of 2.04.
2. Count the places the decimal point moves.

Question 18. Express 0.00056 in standard form.
Answer:
0.00056 = 5.6 × 10⁻⁴, because the decimal point moves 4 places to the right.

Teacher's Note:
1. Moving the decimal point to the right gives a negative exponent.
2. The coefficient must be at least 1.

Question 19. Write 3056 in expanded form using powers of 10.
Answer:
3056 = (3 × 10³) + (0 × 10²) + (5 × 10¹) + (6 × 10⁰).

Teacher's Note:
1. Each place has its own power of 10.
2. Show the zero in the hundreds place.

Question 20. Which is greater, 8.3 × 10⁷ or 9.1 × 10⁶? Give the reason in one line.
Answer:
8.3 × 10⁷ is greater, because in standard form the number with the larger exponent is larger (8 digits against 7 digits).

Teacher's Note:
1. Compare exponents first; coefficients only if exponents are equal.
2. 9.1 being bigger than 8.3 does not matter here.

Question 21. How many times larger than 5⁻² is 5³?
Answer:
5³ ÷ 5⁻² = 5^{3 − (−2)} = 5⁵ = 3125, so 5³ is 3125 times 5⁻².

Teacher's Note:
1. 'How many times larger' means divide.
2. Subtracting a negative exponent adds.

Question 22. Simplify (m⁴)³ ÷ m⁷ and write the answer in exponential form.
Answer:
(m⁴)³ ÷ m⁷ = m¹² ÷ m⁷ = m^{12 − 7} = m⁵.

Teacher's Note:
1. Do the power of a power first.
2. Then subtract exponents for the division.

Question 23. In a pond the number of lotuses triples every day, starting from 1 lotus. Write the number of lotuses after 6 days in exponential form and give its value.
Answer:
The count is multiplied by 3 each day, so after 6 days there are 3⁶ = 729 lotuses.

Teacher's Note:
1. Tripling 6 times means multiplying by 3 six times.
2. Start count 1 means no extra factor.

Question 24. The Jaina treatise Amalasiddhi names every power of ten up to dasha-ananta. Write dasha-ananta as a power of 10.
Answer:
Dasha-ananta is 10⁹⁶, the highest power of ten named in that treatise.

Teacher's Note:
1. This fact comes from the chapter's history section.
2. It shows how far Indian number names went.

Question 25. Simplify \( \frac{2^{-3} \times 6^{4}}{3^{4}} \) and write the answer as a power of 2.
Answer:
\( \frac{2^{-3} \times 6^{4}}{3^{4}} \) = 2⁻³ × \( \left(\frac{6}{3}\right)^{4} \) = 2⁻³ × 2⁴ = 2¹, that is 2.

Teacher's Note:
1. 6⁴ ÷ 3⁴ = (6 ÷ 3)⁴ since the exponents are equal.
2. Then add the exponents of 2.

Question 26. Find the units digit of the value of 7⁸ ÷ 49².
Answer:
49² = (7²)² = 7⁴, so 7⁸ ÷ 49² = 7⁴ = 2401, whose units digit is 1.

Teacher's Note:
1. Write 49 as a power of 7 first.
2. 7⁴ = 2401.

Question 27. If 2^x = 128, find x and then write the value of 2^{x − 3}.
Answer:
2⁷ = 128, so x = 7; then 2^{x − 3} = 2⁴ = 16.

Teacher's Note:
1. Know the powers of 2 up to 2¹⁰ = 1024.
2. Also 128 ÷ 2³ = 16.

Question 28. A factory wants an identity code made only of the digits 0 to 9 for each of its 2 crore items. What is the least number of digits the code must have?
Answer:
An n-digit code gives 10ⁿ codes. 10⁷ = 1 crore is too few, while 10⁸ = 10 crore is enough, so at least 8 digits are needed.

Teacher's Note:
1. Each digit place has 10 choices.
2. Find the smallest power of 10 that is at least 2 crore.

Question 29. Which is longer, 10⁹ seconds or 25 years? Write the comparison in one line.
Answer:
10⁹ seconds is about 31.7 years, so 10⁹ seconds is longer than 25 years.

Teacher's Note:
1. One year is about 3.15 × 10⁷ seconds.
2. Convert to the same unit before comparing.

Question 30. A ladder to the Moon needs about 1.922 × 10⁹ steps, while a sheet of paper reaches the Moon in 46 folds. Name the kind of growth in each case and state the difference between them.
Answer:
The ladder shows linear (additive) growth: a fixed 20 cm is added with each step. The paper shows exponential (multiplicative) growth: the thickness is multiplied by 2 each time. That is why 46 folds beat about 192 crore steps.

Teacher's Note:
1. Linear adds the same amount; exponential multiplies by the same number.
2. Exponential growth soon overtakes linear growth.