Important Questions on Power Play for Class 8

Power Play Class 8 Important Questions & Answers are available in this Maths article. Power Play Class 8 Important Questions & Answers are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Power Play. Power Play covers laws of exponents, writing numbers in powers of 10, and using negative and zero exponents, which we use in everyday calculations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination.

Table of Contents

• What is Power Play (Exponents and Powers)?
• Exercise 13.1: Laws of Exponents (Multiplication and Division)
• Exercise 13.2: Negative Exponents and Laws
• Exercise 13.3: Standard Form (Scientific Notation)
• Exercise 13.4: Comparing Numbers and Mixed Problems
• Tips for Understanding Power Play for Class 8
• Important Questions on Power Play for Class 8

What is Power Play (Exponents and Powers)?

Power Play is the common name given to the chapter on Exponents and Powers in Class 8 Mathematics. This chapter teaches you how to write very large or very small numbers in a short form using powers and exponents. It builds on the basic idea that multiplying a number by itself repeatedly can be written as a power.

For example, instead of writing 2 x 2 x 2 x 2 x 2, you simply write 2 to the power 5, or 25 . The number 2 here is called the base, and 5 is called the exponent or power.

Exercise 13.1: Laws of Exponents (Multiplication and Division)

Question 1: Simplify23x24

Both numbers have the same base, which is 2. Apply Law 1 and add the exponents.23x24= (3 + 4)=27. Now compute27 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128.

Answer:27= 128

Question 2: Simplify56/52

Both numbers have the same base, which is 5. Apply Law 2 and subtract the exponents.56/52=5(6−2)=54. Now compute54 = 5 x 5 x 5 x 5 = 625.

Answer:54= 625

Question 3: Simplify(32)3

A power is raised to another power. Apply Law 3 and multiply the exponents.(32)3 =3(2×3)=36. Now compute36= 729.

Answer:  36= 729

Question 4: Simplify(2×5)3

A product is raised to a power. Apply Law 4 and give the power to each factor(2×5)3=23×53. Now compute23= 8 and53= 125. Multiply: 8 x 125 = 1000.

Answer: 1000

Question 5: Find the value of(70+40)×32

Apply the zero exponent law.70= 1 and40 = 1. So(1+1)×32=2×9=18

Answer: 18

Important Questions: Exercise 13.1

Question: What is the value of any number raised to the power zero? Any non-zero number raised to the power zero is always equal to 1. This is one of the most tested rules in the chapter.

Question: If 2^x = 32, find the value of x. Write 32 as a power of 2. Since 32 = 2 x 2 x 2 x 2 x 2 = 2^5, we get x = 5.

Question: Simplify (a^3 x a^4) / a^5 Add the exponents in the numerator first: a^3 x a^4 = a^7. Then divide: a^7 / a^5 = a^(7-5) = a^2.

Exercise 13.2: Negative Exponents and Laws

Question 1: Express3−4as a fraction

A negative exponent means take the reciprocal3−4=134 . Now compute34 = 3 x 3 x 3 x 3 = 81.

Answer:1/81

Question 2: Simplify2−3×25

Same base, so add the exponents.2−3×25=2(−3+5)=22=4

Answer: 4

Question 3: Simplify5−2×5453

Numerator same base, add exponents:5−2×54=5(−2+4)=52. Now divide:  5253=5(2−3)=5−1and5−1=15

Answer:1/5

Question 4: Find the value of (23)−2

A negative exponent on a fraction means flip the fraction(23)−2=(32)2. Now compute(32)2=3222=94.

Answer: 9/4

Question 5: Express 0.0001 as a power of 10

Write 0.0001 as a fraction: 0.0001 = 1/10000. Write 10000 as a power of 10: 10000 =104. So 1/10000 =1104=10−4.

Answer: 0.0001 = 10−4

Important Questions: Exercise 13.2

Question: Express1/625using a negative exponent with base 5. 625 =54, so1/625 =1/54=5−4.

Question: Simplify  10−3×10510=  102. Then102101 =10(2−1) =101= 10.

Question: Is2−3 equal to (−2)3? Explain. No.  2−3= 1/8which is positive. But  (−2)3 = − 8 which is negative. They are not equal.

Exercise 13.3: Standard Form (Scientific Notation)

Question 1: Express 56,000,000 in standard form

The number is 56,000,000. Move the decimal point to get a number between 1 and 10. 56,000,000 becomes 5.6 the decimal moved 7 places to the left. Since we moved left, the power of 10 is positive 7.

Answer: 5.6 x107

Question 2: Express 0.000042 in standard form

The number is 0.000042. Move the decimal point to get a number between 1 and 10. 0.000042 becomes 4.2 the decimal moved 5 places to the right. Since we moved right, the power of 10 is negative 5.

Answer: 4.2 x10−5

Question 3: Convert 3.6 x104back to a regular number

The power of 10 is 4, which is positive. A positive power means move the decimal point 4 places to the right. 3.6 becomes 36,000.

Answer: 36,000

Question 4: The mass of Earth is 5,970,000,000,000,000,000,000,000 kg. Write in standard form.

Count the digits after the first digit (5). There are 24 digits after 5, so the decimal moves 24 places. The result is 5.97 x1024.

Answer: 5.97 x 1024 kg

Question 5: The size of a hydrogen atom is 0.000000000106 m. Write in standard form.

Move the decimal right until we have a number between 1 and 10. 0.000000000106 becomes 1.06 moved 10 places to the right. Power is negative 10 because we moved right.

Answer: 1.06 x10−10 m

Important Questions: Exercise 13.3

Question: What is the difference between 10^6 and 10^(-6)? 10^6 = 1,000,000 which is one million a very large number. 10^(-6) = 0.000001 which is one millionth a very small number. The negative exponent gives the reciprocal.

Question: A bacteria is 0.0000015 m long. Express this in standard form. Move the decimal 6 places to the right: 1.5. The power is negative 6. Answer: 1.5 x 10^(-6) m.

Question: Add 3 x 10^4 and 2 x 10^4. When the powers of 10 are the same, just add the values: (3 + 2) x 10^4 = 5 x 10^4 = 50,000.

Exercise 13.4: Comparing Numbers and Mixed Problems

Question 1: Arrange in ascending order 4 x 10^5, 3 x 10^7, 8 x 10^3, 2 x 10^7

Compare powers first 10^3, 10^5, 10^7, 10^7. Numbers with smaller powers come first. For the two numbers with 10^7, compare K values 2 and 3. So 2 x 10^7 is less than 3 x 10^7.

Answer: 8 x 10^3, 4 x 10^5, 2 x 10^7, 3 x 10^7

Question 2: The distance from the Earth to the Sun is about 1.5 x 10^11 m. Express as a regular number.

Power is 11, which is positive. Move the decimal point 11 places to the right. 1.5 becomes 150,000,000,000.

Answer: 150,000,000,000 metres

Question 3: Simplify (2^3 x 3^2) / (2^2 x 3^3)

Deal with powers of 2 separately: 2^3 / 2^2 = 2^(3-2) = 2^1 = 2. Deal with powers of 3 separately: 3^2 / 3^3 = 3^(2-3) = 3^(-1) = 1/3. Multiply the results: 2 x 1/3 = 2/3.

Answer: 2/3

Question 4: If 5^(2x-1) = 5^7, find the value of x.

Since the bases are equal, the exponents must be equal. Set 2x - 1 = 7. Then 2x = 8. So x = 4.

Answer: x = 4

Question 5: A light year is 9.46 x 10^15 m. The nearest star is 4.22 light years away. How far is it in metres?

Distance = 4.22 x (9.46 x 10^15). Multiply the K values: 4.22 x 9.46 = 39.92. Keep the power of 10: 39.92 x 10^15. Convert to proper standard form: 3.992 x 10^16.

Answer: Approximately 3.99 x 10^16 metres

Tips for Understanding Power Play for Class 8

• Understand the Meaning, Not Just the Rule

• Never Mix Bases.

• Learn the Trick for Standard Form

• Use the Zero Rule as a Check

• Negative Exponent Means Flip

• Practise Writing Numbers in Both Directions

• Make a Laws Summary Card

• 8Solve from the Inside Out

Important Questions on Power Play for Class 8

These questions come from the most frequently tested areas in this chapter. They cover all types direct formula application, word problems, proofs, and standard form conversions.

Short Answer Important Questions (1 to 2 Marks)

Question 1: What is the value of 10^0? Answer: Any number raised to the power zero equals 1. So 10^0 = 1.

Question 2: Express 1/49 as a power of 7. Answer: 49 = 7^2, so 1/49 = 1/7^2 = 7^(-2).

Question 3: Simplify 2^4 x 2^3 / 2^5 Answer: 2^4 x 2^3 = 2^7. Then 2^7 / 2^5 = 2^2 = 4.

Question 4: Write 93,000,000 in standard form. Answer: Move the decimal 7 places left: 9.3 x 10^7.

Question 5: Write 7^(-3) without a negative exponent. Answer: 7^(-3) = 1/7^3 = 1/343.

Long Answer Important Questions (3 to 5 Marks)

Question 6: Prove that (x^a / x^b)^(a+b) x (x^b / x^c)^(b+c) x (x^c / x^a)^(c+a) = 1

Apply the division law inside each bracket. x^a / x^b = x^(a-b), x^b / x^c = x^(b-c), x^c / x^a = x^(c-a). Raise each to its power using the power-of-a-power law.

(x^(a-b))^(a+b) = x^((a-b)(a+b)) = x^(a^2 - b^2) (x^(b-c))^(b+c) = x^(b^2 - c^2) (x^(c-a))^(c+a) = x^(c^2 - a^2)

Multiply all three same base, so add exponents: x^(a^2 - b^2 + b^2 - c^2 + c^2 - a^2). All terms cancel in the exponent, giving x^0 = 1.

Answer: Proved the expression equals 1.

Question 7: The distance between two planets is 3.84 x 10^8 m. A spacecraft travels at 4.8 x 10^3 m per second. How long does it take to reach the planet?

Time = Distance / Speed. Time = (3.84 x 10^8) / (4.8 x 10^3). Divide the K values: 3.84 / 4.8 = 0.8. Divide the powers: 10^8 / 10^3 = 10^5. So time = 0.8 x 10^5 = 8 x 10^4 seconds.

Answer: 8 x 10^4 seconds (which is 80,000 seconds or about 22.2 hours).

Question 8: If 4^(x+3) = 256, find x.

Write 256 as a power of 4: 256 = 4 x 4 x 4 x 4 = 4^4. Since bases are equal, x + 3 = 4. So x = 1.

Answer: x = 1

Most Common Examination Questions (Board Exams)

Direct Law Application (Most Frequent)

These questions ask you to simplify an expression using one or more laws of exponents. They appear in nearly every exam.

Board Question: Simplify (3^(-4) x 3^7) / (3^2 x 3^(-5))

Numerator: 3^(-4) x 3^7 = 3^(-4+7) = 3^3. Denominator: 3^2 x 3^(-5) = 3^(2-5) = 3^(-3). Division: 3^3 / 3^(-3) = 3^(3-(-3)) = 3^6. And 3^6 = 729.

Answer: 729

Standard Form Conversion (Very Frequent)

Board Question: Express the speed of light (299,792,458 m/s) in standard form.

The first digit is 2. Move the decimal after 2: 299,792,458 becomes approximately 3.0 (rounded). Count digits moved: 8 places to the left. Power is positive 8.

Answer: Approximately 3.0 x 10^8 m/s

Finding the Unknown (Frequent)

Board Question: If 2^(3x-1) = 2^5, find x.

Bases are equal so exponents must be equal: 3x - 1 = 5. So 3x = 6, and x = 2.

Answer: x = 2

Word Problems Using Standard Form (Frequent)

Board Question: Mass of the Earth = 5.97 x 10^24 kg. Mass of the Moon = 7.35 x 10^22 kg. How many times heavier is the Earth than the Moon?

Divide Earth mass by Moon mass: (5.97 x 10^24) / (7.35 x 10^22). Divide K values: 5.97 / 7.35 = approximately 0.812. Divide powers: 10^24 / 10^22 = 10^2 = 100. So 0.812 x 100 = 81.2.

Answer: The Earth is approximately 81 times heavier than the Moon.

Proof Based Questions (Occasional)

Board Question: If a = 2 and b = 3, verify that (a+b)^2 is not equal to a^2 + b^2.

Calculate (a+b)^2 = (2+3)^2 = 5^2 = 25. Calculate a^2 + b^2 = 2^2 + 3^2 = 4 + 9 = 13. Since 25 is not equal to 13, it is verified.

Answer: Verified (a+b)^2 does not equal a^2 + b^2.