Important Questions Class 8 Maths Ganita Prakash – I Chapter 2 Power Play

SHORT QUESTIONS

Question 1. What is the thickness after 3 folds if initial thickness is 0.001 cm?

Solution:
Thickness doubles each time
= 0.001 × 2³
= 0.001 × 8
= 0.008 cm

Answer: 0.008 cm

Question 2. Express 2 × 2 × 2 × 2 × 2 in exponential form.

Solution:
2 multiplied 5 times = 2⁵

Answer: 2⁵

Question 3. Find the value of 2¹⁰.

Solution:
2¹⁰ = 1024

Answer: 1024

Question 4. Write 32400 in exponential form using prime factors.

Solution:
32400 = 2⁴ × 3⁴ × 5²

Answer: 2⁴ × 3⁴ × 5²

Question 5. What is (−1)⁵?

Solution:
Odd power → negative
= −1

Answer: −1

Question 6. Simplify: 2⁴ ÷ 2²

Solution:
2⁴⁻² = 2² = 4

Answer: 4

Question 7.  What is 10⁵?

Solution:
10⁵ = 100000

Answer: 100000

Question 8. Write 5900 in scientific notation.

Solution:
5900 = 5.9 × 10³

Answer: 5.9 × 10³

Question 9. What is 2⁰?

Solution:
Any number⁰ = 1

Answer: 1

Question 10. Find 3⁴ × 3²

Solution:
3⁴⁺² = 3⁶ = 729

Answer: 729

LONG QUESTIONS

Question 1. Find the thickness of paper after 10 folds if initial thickness is 0.001 cm.

$T = 0.001 \times 2^{10}$

Solution:
2¹⁰ = 1024
T = 0.001 × 1024
= 1.024 cm

Answer: 1.024 cm

Question 2. A pond doubles the number of lotuses every day. If it is full on day 30, when was it half full?

Solution:
Doubling pattern → previous day is half
So, half full on day 29

Answer: Day 29

Question 3. Find total number of diamonds if pattern is 3 × 3 × 3 × 3 × 3 × 3 × 3

$3^7$

Solution:
3⁷ = 2187

Answer: 2187 diamonds

Question 4. Find number of possible passwords in a 5-digit lock.

$10^5$

Solution:
Each digit has 10 choices
Total = 10⁵ = 100000

Answer: 100000 passwords

Question 5. Simplify: 2⁴ × 2³ × 2⁻²

$2^{4+3-2}$

Solution:
= 2⁵
= 32

Answer: 32