Maths 8 Chapter Wise | Exponents & Problem-Solving Guide

Mastering Math Fundamentals: Your Guide to Exponents and Problem-Solving

A chapter-wise Class 8 guide covering problem-solving strategies, exponents, laws of exponents, and scientific notation with examples.

• 1. Strategy for Solving Any Problem
• 2. Understanding the Power of Exponents
• 3. Essential Laws of Exponents
• 4. Handling Massive Numbers

1. Strategy for Solving Any Problem

1. Understand the problem: Identify knowns, unknowns, and what’s asked.
2. Plan your approach: Choose methods, formulas, or models that fit.
3. Execute: Apply steps carefully; make reasonable approximations when needed.
4. Review: Check the result and reflect on improvements.

2. Understanding the Power of Exponents

Exponentiation (घातांकन) is repeated multiplication. If you have \(n^a\), it means multiplying \(n\) by itself \(a\) times.

Negative exponents form reciprocals: \(n^{-a} = \frac{1}{n^a}\).

3. Essential Laws of Exponents

• Same base (multiply): \(n^a \times n^b = n^{a+b}\)
• Power of a power: \((n^a)^b = n^{a\times b}\)
• Same base (divide): \(n^a \div n^b = n^{a-b}\) where \(n eq 0\)
• Same exponent (multiply): \(n^a \times m^a = (n \times m)^a\)
• Same exponent (divide): \(n^a \div m^a = \left(\frac{n}{m}\right)^a\) where \(m eq 0\)
• Zero exponent: \(n^0 = 1\) for \(n eq 0\)

Examples:

• \(2^3 \times 2^4 = 2^{7} = 128\)
• \((3^2)^3 = 3^{6} = 729\)
• \(5^5 \div 5^2 = 5^{3} = 125\)
• \(4^2 \times 3^2 = (4 \times 3)^2 = 12^2 = 144\)
• \(8^3 \div 2^3 = \left(\frac{8}{2}\right)^3 = 4^3 = 64\)
• \(7^0 = 1\)

4. Handling Massive Numbers

Use scientific notation to express scale: \(x \times 10^y\) where \(1 \le x < 10\) and \(y\) is an integer.

• Example: 300,000,000 → \(3 \times 10^8\)
• Earth receives about \(2 \times 10^{-9}\) of the Sun’s energy output.

Explore more in our Maths 8 Chapter Wise series.

4. The value of n−a is equal to:

1. −na

2. na

3. 1 / n−a

4. 1 / na

Answer: D

5. Operations with exponents satisfy the rule na × nb =

1. na×b

2. na/b

3. na+b

4. (n×n)a+b

Answer: C

6. Operations with exponents satisfy the rule (na)b =

1. na+b

2. na−b

3. na×b

4. na/b

Answer: C

7. If n ≠ 0, simplify na ÷ nb :

1. na+b

2. na−b

3. na×b

4. na/b

Answer: B

8. Simplify na × ma :

1. (n+m)a

2. na+m

3. (n×m)a

4. na×m

Answer: C

9. If m ≠ 0, simplify na ÷ ma :

1. (n×m)a

2. na−m

3. (n÷m)a

4. na/m

Answer: C

10. If n ≠ 0, what is the value of n0?

1. n

2. 0

3. nn

4. 1

Answer: D

Scientific Notation

11. The scientific notation for the number 308100000 is:

1. 30.81 × 107

2. 3.081 × 109

3. 3.081 × 108

4. 308.1 × 106

Answer: C

12. In the standard form of scientific notation (x × 10y), the value of x must satisfy which condition?

1. x > 10

2. x ≤ 1

3. 1 ≤ x < 10

4. x can be any real number

Answer: C

13. In the standard form of scientific notation (x × 10y), y is defined as what type of number?

1. A positive rational number

2. A whole number

3. An integer

4. A prime number

Answer: C

Problem Solving and Estimation

14. The general problem-solving approach involves making assumptions and approximations to carry out the...

1. Modeling

2. Guessing

3. Questioning

4. Calculations

Answer: D

15. To understand how large a number or quantity is, one can engage in:

1. Rapid additive growth

2. Simple division

3. Interesting thought experiments

4. Comparing cube and square numbers

Answer: C

Educational MCQ Series | Maths8Chapterwise.blogspot.com

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