E ExamMaster

CBSE Class 8 · Mathematics

Power Play

Official NCERT chapter from Ganita Prakash Part I (book code hegp1). ExamMaster notes are original teaching at CBSE Class 8 depth.

This lesson follows the official chapter “Power Play” in Ganita Prakash Part I. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 8
  • Easy level
  • 8 concepts

1Experiencing the Power Play

A power is repeated multiply of the same base: 2⁵ is 2×2×2×2×2 = 32, not 2×5. Experiencing the play is writing a few and seeing how fast they grow.

2⁵ is not 10. The little 5 counts copies of the base, not a multiply by 5.

Figure. The power play is doubling: 2^0=1, then 2, 4, 8, 16. Each step multiplies by the same base. The pile grows much faster than adding 2 each time.

How it works

  1. Write the base and the index2 and 5.
  2. Multiply that many copies of the baseFive 2s.
  3. Read 32, not 10The power.

2Exponential Notation and Operations

When bases match: a^m × a^n = a^{m+n}, a^m ÷ a^n = a^{m-n} (a ≠ 0), and (a^m)^n = a^{mn}. The operations sit on the indices.

2³ × 2⁴ is 2⁷ = 128, not 2¹² and not 4⁷.

Figure. Exponential notation packs a repeated product. Four factors of 2 are 2\times2\times2\times2, and that is exactly 2^4. The small raised 4 counts the factors.

How it works

  1. Check the bases matchSame a.
  2. For × add indices; for ÷ subtract; for a power of a power multiply indicesThe job.
  3. Evaluate if you need a value2⁷ = 128.

Same base

Simplify 3² × 3³ and evaluate.

  • Add indices3⁵
  • 3⁵243
  • Not 3⁶2+3=5, not 2×3

Pro tip. Same base: add the indices for a product.

3The Other Side of Powers

A negative index means a reciprocal: a⁻ⁿ = 1/aⁿ (a ≠ 0). 2⁻³ = 1/8. The other side of powers is “how many times you divide by the base”, not a negative answer for a positive base.

2⁻³ is not −8.

Figure. The other side of the same play is dividing by the base. From 2^3=8 down through 2^0=1 you reach 2^{-1}=1/2. Negative exponents are not a new operation; they continue the ÷2 steps.

How it works

  1. See a negative index−3 on base 2.
  2. Write 1 over the positive power1/2³ = 1/8.
  3. Refuse a minus on the value just because the index is minusReciprocal, not sign-flip.

4Powers of 10

Powers of 10 are house-shifts: 10³ = 1000 (three zeros), 10⁻² = 0.01 (point two places). Scientific writing later uses this; here, count zeros or houses.

10³ is not 30.

Figure. Powers of 10 are place-value steps. Each extra exponent multiplies by 10, so 10, 100, 1000, and 10000 sit one decade apart. A linear axis would hide the first bars; the scale is decades.

How it works

  1. For 10ⁿ with n > 0, write 1 and n zeros1000.
  2. For 10⁻ⁿ, put 1 in the n-th house after the point0.01 for n=2.
  3. Keep 10 as the base — 2³ is a different playTens-houses.

5Did You Ever Wonder?

Wonder here is a question you can put on a power: how many zeros in 10⁴? Why 2¹⁰ is 1024, not 20? The wonder ends in a write.

Wondering without multiplying is a poster.

Figure. 2^{10}=1024 sits next to 10^3=1000. That is why people remember “kilo” as about 2^{10} in computing and as exactly 1000 in SI. The two powers are close, not equal.

How it works

  1. Ask a power-questionWhat is 2⁴? How many zeros in 10⁵?
  2. Write the repeated multiply or the zero-countThe play.
  3. Answer in a number16, or five zeros.

6A Pinch of History

People wrote large repeats with a small index for a long time. History is a pinch. It does not evaluate 2⁵ for you.

A famous name is not 32.

Figure. Older writing listed the factors. Index form writes the same product as a base and a count. 2\cdot2\cdot2\cdot2 and 2^4 are one number, 16.

How it works

  1. Keep the pinch as a noteThe writing is old.
  2. Return to this base and index2⁵.
  3. MultiplyHistory is not the product.

7A definition is a test you can run

A power is a test: same base, a count of copies. If you cannot write the product, you have a decoration 2⁵ only.

A tiny 5 printed prettily is not 32.

Figure. The definition is a test you can run: a^n means n factors of a. For 3^4 write four threes and multiply. The product is 81, not 3\times4=12.

How it works

  1. Write the copies2·2·2·2·2.
  2. MultiplyThe test.
  3. If you treat the index as a factor, you failed the definition2×5 is the miss.

8Name the given before the unknown

The given are the base and the index (or two powers to combine). The unknown is the value or the simplified power. Copy the base before you add indices.

Adding indices when bases differ (2³ × 3²) is a silent given you invented.

Figure. Name the given before the unknown. In 5^3 the base is 5 and the exponent is 3. Only then compute 5\times5\times5=125. Swapping them asks a different question.

How it works

  1. Copy bases and indicesThe given.
  2. Name value or simplifyThe unknown.
  3. Same-base rules only when bases matchGiven first.
2³ × 2⁴ equals
  1. 2⁷ = 128
  2. 2¹²
  3. 4⁷

Same base: add indices.

Notes

  • The official chapter title is “Power Play”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • aᵐ × aⁿ = aᵐ⁺ⁿ (same base)
  • a⁻ⁿ = 1/aⁿ (a ≠ 0)
  • 10ⁿ = 1 followed by n zeros (n > 0)

Recap

Hold these pegs from the official chapter “Power Play”. The wording is ExamMaster’s teaching, not a textbook recap.

Experiencing the Power Play
A power is repeated multiply of the same base: 2⁵ is 2×2×2×2×2 = 32, not 2×5.
Exponential Notation and Operations
When bases match: a^m × a^n = a^{m+n}, a^m ÷ a^n = a^{m-n} (a ≠ 0), and (a^m)^n = a^{mn}.
The Other Side of Powers
A negative index means a reciprocal: a⁻ⁿ = 1/aⁿ (a ≠ 0).
Powers of 10
Powers of 10 are house-shifts: 10³ = 1000 (three zeros), 10⁻² = 0.01 (point two places).
Did You Ever Wonder?
Wonder here is a question you can put on a power: how many zeros in 10⁴? Why 2¹⁰ is 1024, not 20? The wonder ends in a write.
A Pinch of History
People wrote large repeats with a small index for a long time.

Practise Power Play

Reading is free and needs no account. Practice, mocks and progress live in the app.

  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
Continue with Google — freeNo card, no trial. Works offline once installed.