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MathematicsClass 8Power Play

Power Play | Class 8 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 4 min read

Power Play – this guide gives you a concise, exam-ready overview of Power Play from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

Laws of Exponents

This section elaborates on the fundamental laws of exponents that govern how powers behave during multiplication, division, and raising a power to another power. These laws help simplify expressions involving powers and are essential for solving algebraic problems efficiently. The key laws introduced are:

1. Product Law: When multiplying two powers with the same base, add the exponents. For example, a^m × a^n = a^(m+n).

2. Quotient Law: When dividing two powers with the same base, subtract the exponents. For example, a^m ÷ a^n = a^(m−n), provided a ≠ 0.

3. Power of a Power Law: When raising a power to another power, multiply the exponents. For example, (a^m)^n = a^(m×n).

4. Power of a Product Law: The power of a product is the product of the powers. For example, (ab)^m = a^m × b^m.

5. Power of a Quotient Law: The power of a quotient is the quotient of the powers. For example, (a/b)^m = a^m ÷ b^m, provided b ≠ 0.

These laws apply for any real number base (except zero in division) and integer exponents. The section provides detailed proofs and examples to illustrate each law, emphasizing their use in simplifying expressions and solving problems.

📊 Diagram: Diagrams illustrate multiplication and division of powers with the same base, showing how exponents add or subtract. Another figure shows a power raised to another power, demonstrating multiplication of exponents.

🧪 Activity: Activity: Students are asked to verify the laws of exponents by calculating powers using repeated multiplication and then using the laws to confirm the results.

🔗 Connection: This section sets the stage for the next topic, which deals with negative exponents and zero exponents, expanding the understanding of powers.

Frequently asked questions

1. Find out the units digit in the value of 2224 ÷ 432? [Hint: 4 = 22]

To find the units digit of 2224 ÷ 432, first note that 4 = 22. This implies 4 is 2 squared. The question likely means to find the units digit of 2 raised to the power 224 divided by 4 raised to the power 32, or possibly 2^224 divided by 4^32. Since 4 = 2^2, 4^32 = (2^2)^32 = 2^(64). So the expression is 2^224 ÷ 2^64 = 2^(224-64) = 2^160. The units digit of powers of 2 cycle every 4 powers: 2^1=2, 2^2=4, 2^3=8, 2^4=6, then repeats. 160 mod 4 = 0, so units digit is 6.

2. There are 5 bottles in a container. Every day, a new container is brought in. How many bottles would be there after 40 days?

Each container has 5 bottles. Every day, one new container is added. After 40 days, number of containers = 40. Total bottles = 40 × 5 = 200 bottles.

3. Write the given number as the product of two or more powers in three different ways. The powers can be any integers. (i) 643 (ii) 1928 (iii) 32–5

For each number, express as product of powers in three different ways:

(i) 643

  • 64 = 8^2 = 4^3 = 2^6
  • So possible products:

1) 8^2 2) 4^3 3) 2^6

(ii) 1928

  • 1928 = 19 × 28
  • 19 is prime, 28 = 2^2 × 7
  • Possible products:

1) 19 × 28 2) (19 × 2)^2 × 7^{-1} (not integer power, so avoid) 3) 19^1 × (2^2 × 7)^1

(iii) 32^{-5}

  • 32 = 2^5
  • So 32^{-5} = (2^5)^{-5} = 2^{-25}
  • Possible products:

1) 2^{-25} 2) (2^{-5})^{5} 3) (2^{-1})^{25}

4. Examine each statement below and find out if it is ‘Always True’, ‘Only Sometimes True’, or ‘Never True’. Explain your reasoning. (i) Cube numbers are also square numbers. (ii) Fourth powers are also square numbers. (iii) The fifth power of a number is divisible by the cube of that number. (iv) The product of two cube numbers is a cube number. (v) q46 is both a 4th power and a 6th power (q is a prime number).

(i) Cube numbers are also square numbers.

  • Only sometimes true. For example, 64 = 4^3 = 8^2 is both cube and square, but 8 = 2^3 is not a square.

(ii) Fourth powers are also square numbers.

  • Always true. Because (n^2)^2 = n^4, so fourth powers are squares of squares.

(iii) The fifth power of a number is divisible by the cube of that number.

  • Always true. Since n^5 = n^3 × n^2, n^5 is divisible by n^3.

(iv) The product of two cube numbers is a cube number.

  • Always true. Since a^3 × b^3 = (

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