Power Play Class 8 Extra Questions Maths Chapter 2

During revision, students quickly go through Class 8 Maths Extra Questions Chapter 2 Power Play Class 8 Extra Questions with Answers for clarity.

Class 8 Power Play Extra Questions

Class 8 Maths Chapter 2 Power Play Extra Questions

Class 8 Maths Chapter 2 Extra Questions – Power Play Extra Questions Class 8

Question 1.
Simplify: \(\left(4^0+2^0\right)^0 \div\left(\frac{1}{2}\right)^{-2}\)
Solution:

Question 2.
Simplify: \(\left(4^2 \times 2^{-3}\right) \div\left(\frac{1}{10}\right)^{-2}\)
Solution:

Question 3.
Write the following in expanded form using exponents of 10.
(a) 425.2394
(b) 76.359898
Solution:

Question 4.
Express the numbers used in the following facts in scientific notation.
(a) The speed of light is 300000000 m/s.
(b) The distance from the Earth to the Moon is 384400000 m.
Solution:
(a) The speed of light = 300000000 m/s = 3 × 10⁸ m/s.
(b) The distance from the Earth to the Moon = 384400000 m = 3.844 × 10⁸ m.

Question 5.
If the mass of the Earth is 5.97 × 10²⁴ kg and the mass of the Moon is 7.35 × 10²² kg, which is heavier and by how much?
Solution:
Here, we have to compare the mass of the Earth and the Moon.
We will convert them into numbers with the same exponents 22, as 22 < 24.
Mass of Earth = 5.97 × 10²⁴ kg
= 5.97 × 100 × 10²²
= 597 × 10²² kg
Mass of Moon = 7.35 × 10²² kg
Since 597 × 10²² kg > 7.35 × 10²² kg.
So, Earth is heavier than the Moon.
Further, the difference of masses = (597 × 10²² kg) – (7.35 × 10²² kg)
= (597 – 7.35) × 10²² kg
= 589.65 × 10²² kg
= 5.8965 × 10²⁴ kg
Hence, the Earth is approximately 5.8965 × 10^24 kg heavier than the Moon.

Question 6.
Express the height of a bundle of 500 papers placed on each other if the thickness of one paper is 0.0016 cm, in standard form.
Solution:
Number of papers = 500
Thickness of one paper = 0.0016 cm
Total height = Number of papers × Thickness of one paper
= 500 × 0.0016 cm
= 0.8 cm
= 8 × 10^-1 cm
Therefore, the height of the bundle of 500 papers is 8 × 10^-1 cm.

Practice Questions

Question 1.
Convert the following to exponential form:
(a) 8 × 8 × 8 × 8
(b) z × z
(c) 4 × 4 × 6 × 6 × 6
(d) m × m × m × m × m × g × g × g
(e) 3 × 3 × p × p
Answer:
(a) 8⁴
(b) z²
(c) 4² × 6³
(d) m⁵ × g³
(e) 3² × p²

Question 2.
Write the following as a product of their prime factors using powers.
(a) 924
(b) 875
(c) 1080
(d) 242
(e) 735
Answer:
(a) 2² × 3 × 7 × 11
(b) 5³ × 7
(c) 2³ × 3³ × 5
(d) 2 × 11²
(e) 3 × 5 × 7²

Question 3.
Find the actual value of these expressions:
(a) 5 × 10²
(b) 6² × 2³
(c) 4 × 3⁴
(d) (-4)² × (-6)²
(e) (-3)³ × (-2)⁴
Answer:
(a) 500
(b) 288
(c) 324
(d) 576
(e) -432

Question 4.
What is the units digit of the result of this expression: 3²⁴⁵ ÷ 9⁸⁰?
Answer:
3

Question 5.
Ajar contains 6 marbles. Each day, one more jar with 6 marbles is added. How many marbles will there be after 30 days?
Answer:
180 marbles

Question 6.
Express the number as a product of powers in three different ways.
(You can use positive or negative exponents.)
(a) 81³
(b) 256⁴
(c) 16^-6
Answer:
(a) 3¹², 9⁶, 27³ × 3³
(b) 2³², 16⁸, 4¹⁶
(c) 2^-24, 4^-12, 8^-16 × 2^-6

Question 7.
For each statement below, say whether it is Always True, Only Sometimes True, or Never True. Give a reason for your answer:
(i) Every square number is also a cube number.
(ii) The square of any even number is divisible by 4.
(iii) The sixth power of a number is divisible by its square.
(iv) The product of a cube and a square number is always a cube.
(v) If m²⁴, then mmm must be a square and cube root of that number.
Answer:
(i) Never True
(ii) Always True
(iii) Always True
(iv) Only Sometimes True
(v) Always True

Question 8.
Evaluate the expressions using power laws:
(a) 10^-3 × 10^-6
(b) 6⁸ ÷ 6⁵
(c) 8^-4 ÷ 8^-2
(d) (15^-3)⁴
(e) a⁴ b³ × (ab²)⁵
Answer:
(a) 10^-9
(b) 6³
(c) 8^-2
(d) 15^-12
(e) a⁹ b¹³

Question 9.
Use known squares to find values. If 11² = 121, then find the value of:
(a) (1.1)²
(b) (0.11)²
(c) (0.011)²
(d) 110²
(e) 0.0011²
Answer:
(a) 1.21
(b) 0.0121
(c) 0.000121
(d) 12,100
(e) 0.00000121

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