NCERT Solutions for Class 8 Maths Chapter 10 Exponents and Powers

NCERT Solutions for Class 8 Maths Chapter 10 Exponents and Powers help students understand concepts like laws of exponents, powers with negative exponents, standard form, and scientific notation. These solutions provide clear, step-by-step explanations for all exercise questions. Students can easily practice problems, improve calculation skills, and build strong basics. The solutions follow the latest CBSE syllabus and help in better exam preparation and concept clarity.

Most students find exponents tricky because of floating numbers and negative signs. This chapter is one of the highest-scoring parts of Class 8 Maths after you grasp the basic rules. This guide provides a clear exponents and powers class 8 question answer walkthrough to help you navigate your exams with confidence.

Exponents and Power Explanation in Simple Language

An exponent shows how many times a base is multiplied by itself. In eighth grade, we learn about negative exponents, which say that $a^{-m} = 1 / a^m$. Before you try to answer these questions, be sure you know the basic rules that apply to all exponential calculations.

Summary of Exponent Laws

The table below is a quick guide to the arithmetic rules you will use to make complicated formulas easier to understand:

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Exponents and Powers class 8 Question Answer

Here are detailed solutions to help you master the chapter:

Section 1: Evaluating Numerical Expressions

Question 1: Find the value of (1/3)^{-2} + (1/2)^{-2} + (1/4)^{-2}

• Step 1: Apply the negative exponent rule for fractions: (a/b)^{-m} = (b/a)^m.

• Step 2: Rewrite the terms by taking reciprocals: 3^2 + 2^2 + 4^2.

• Step 3: Calculate: 9 + 4 + 16 = 29.

• Answer: 29.

Question 2: Find the value of \{ (1/3)^{-1} - (1/4)^{-1} \}

• Step 1: First, solve what's inside the curly brackets. The inverse of 1/3 is 3, and the inverse of 1/4 is 4.

• Step 2: The expression becomes (3 - 4)^{-1} = (-1)^{-1}.

• Step 3: The answer is -1 since (-1)^{-1} = 1 / (-1)^1.

• Answer: -1.

Read More - NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Question 3: Simplify (5/8)^{-7} \times (8/5)^{-4}

• Step 1: Make the bases identical. Flip (5/8)^{-7}$ to get $(8/5)^7.

• Step 2: Now apply the Product Law: (8/5)^7 \times (8/5)^{-4} = (8/5)^{7 + (-4)} .

• Step 3: Simplify the power: (8/5)^3.

• Answer: 512 / 125.

Section 2: Finding the Unknown (m)

These types of problems are popular in exponents and powers class 8 question answer pdf downloads, as they test algebraic logic.

Question 4: Find m so that (-3)^{m+1} \times (-3)^5 = (-3)^7

• Step 1: Use the Product Law on the left side: (-3)^{m+1+5} = (-3)^{m+6}.

• Step 2: Set the exponents equal since the bases are identical: m + 6 = 7.

• Step 3: Solve for m: m = 7 - 6 = 1.

• Answer: m = 1.

Question 5: Find the value of m for which 5^m \div 5^{-3} = 5^5

• Step 1: Use the Quotient Law: 5^{m - (-3)} = 5^{m+3}.

• Step 2: Compare with the Right Hand Side (RHS): m + 3 = 5.

• Answer: m = 2.

Section 3: Standard Form (Scientific Notation)

Standard form, which is often called scientific notation, is a means to write numbers that are very big or very small using powers of 10. This is a common subject in multiple-choice questions. 

Question 6: How do you write 0.00000000000942 in standard form?

• Step 1: Move the decimal point to the right until it comes after the first digit that isn't zero (9).

• Step 2: Count the jumps. It takes 12 jumps to reach 9.42.

• Answer: 9.42 \times 10^{-12}.

Question 7: Write 3.61492 \times 10^6 in its normal form.

• Step 1: Move the decimal point 6 places to the right because the power of 10 is 6.

• Answer: 36,14,920.

Section 4: Advanced Simplification and Word Problems

You can see questions using nested brackets or variable bases on competitive tests.

Question 8:  Simplify the expression: [ (1/2) raised to -2 + (1/3) raised to -2 + (1/4) raised to -2 ] divided by 29

• Step 1: Simplify the terms inside the square brackets: 2 squared + 3 squared + 4 squared.

• Step 2:  This indicates that 4+9+16 = 29.

• Step 3: Now, divide the answer by the number that was given in the question: 29 / 29 = 1.

• Answer: 1.

Question 9: How big is a plant cell (0.00001275 m) compared to a red blood cell (0.000007 m)?

• Step 1: Change both of them to standard form so you can easily compare them. One plant cell is 1.275 * 10^-5 m. Red blood cell = 7.0 * 10^-6 m.

• Step 2: To see the difference, divide the bigger number by the smaller number: (1.275 * 10^-5) / (7 * 10^-6).

• Step 3: This simplifies roughly to 1.8. Thus, the plant cell is nearly twice as large as a red blood cell.

Read More - NCERT Solutions for Class 8 Maths Chapter 8 Algebraic Expressions and Identities

Exponents and Powers class 8 Question Answer: Preparation Strategy

1. Prime Factorisation: In this, if you see a base like 4, 8, or 27, convert them to 2^2, 2^3, or 3^3 immediately to simplify the math.

2. Sign Awareness: Remember that (-1)^{even} = 1 and (-1)^{odd} = -1. This is the most common place where students lose marks.

3. PDF Resources: Use the exponents and powers class 8 questions with answers pdf to practice multi-step simplifications and improve your speed.

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