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Tamil Nadu (TNBSE)Class 7 Mathematics★ 6-10 marks in the TN Class 7 Term 2 exam through exponent simplification sums

Algebra (Term 2) - Exponents

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 2 Chapter 3, Algebra (Exponents). The concept of exponents and powers, the laws of exponents (product, quotient, power of a power, same and different bases), the degree of an expression, and the unit digit of numbers in exponential form, with worked examples, exercises and quick revision.

⏱ 14 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Write numbers in exponential form
2Apply the product and quotient laws
3Apply the power-of-a-power law
4Use the zero exponent rule
5Find the degree of an expression and the unit digit of a power

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Why this chapter matters

Exponents give a short way to write repeated multiplication and underlie scientific notation and algebra. The laws of exponents are directly tested in the TN Class 7 Term 2 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Term 1 — Algebra (Expressions)

Terms and powers.

Algebra (Exponents) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 2 — Chapter 3. Powers and the laws of exponents.

1. About this chapter

This chapter covers exponents and powers, the laws of exponents, the degree of an expression, and finding the unit digit of numbers in exponential form.

2. Exponents and powers

An exponent tells how many times a base is multiplied by itself: in a⁵, a is the base and 5 is the exponent (power), so a⁵ = a × a × a × a × a.
Example: 2⁴ = 2 × 2 × 2 × 2 = 16.

3. Laws of exponents

For a non-zero base a and whole numbers m, n:

Law	Rule
Product (same base)	aᵐ × aⁿ = aᵐ⁺ⁿ
Quotient (same base)	aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Power of a power	(aᵐ)ⁿ = aᵐⁿ
Same exponent (product)	aᵐ × bᵐ = (ab)ᵐ
Same exponent (quotient)	aᵐ ÷ bᵐ = (a/b)ᵐ
Zero exponent	a⁰ = 1

4. Degree and unit digit

The degree of an expression is the highest power of the variable in it (e.g. 3x⁴ + 2x has degree 4).
The unit digit of a power follows a repeating pattern, e.g. powers of 2 end in 2, 4, 8, 6, 2, 4, … (cycle of 4).

5. Worked examples

Example 1. Simplify 3² × 3⁴. Same base → 3²⁺⁴ = 3⁶ = 729.

Example 2. Simplify (2³)². Power of a power → 2³ˣ² = 2⁶ = 64.

Example 3. Simplify 5⁷ ÷ 5⁴. Same base → 5⁷⁻⁴ = 5³ = 125.

6. Exercises (Samacheer Kalvi)

Write in exponential form: 7 × 7 × 7 × 7.
Simplify: (a) 2³ × 2⁵ (b) 10⁶ ÷ 10² (c) (3²)³.
Find the value of 4⁰ + 5⁰.
State the degree of 6x⁵ − 2x³ + 9.
Find the unit digit of 2¹⁰.

7. Common mistakes

Mistake: Multiplying the bases when multiplying powers. Fix: 2³ × 2⁴ = 2⁷ (add exponents, keep the base) — not 4⁷.
Mistake: Thinking a⁰ = 0. Fix: Any non-zero base to the power 0 is 1.
Mistake: Multiplying exponents in the product law. Fix: Add exponents for the product law; multiply only for power of a power.

8. Quick revision

Term 2 · Ch 3 · exponents.
aᵐ = a multiplied m times; a⁰ = 1.
Product: aᵐ × aⁿ = aᵐ⁺ⁿ; quotient: aᵐ ÷ aⁿ = aᵐ⁻ⁿ; power of a power: (aᵐ)ⁿ = aᵐⁿ.
Same exponent: aᵐ × bᵐ = (ab)ᵐ. Degree = highest power; unit digits repeat in cycles.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Product law

aᵐ × aⁿ = aᵐ⁺ⁿ

Add exponents.

Quotient law

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

Subtract exponents.

Power of a power

(aᵐ)ⁿ = aᵐⁿ

Multiply exponents.

Zero exponent

a⁰ = 1 (a ≠ 0)

Any non-zero base.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Multiplying the bases when multiplying powers

✓ 2³ × 2⁴ = 2⁷ (add exponents, keep the base), not 4⁷.

WATCH OUT

✗ Thinking a⁰ = 0

✓ Any non-zero base to the power 0 is 1.

WATCH OUT

✗ Multiplying exponents in the product law

✓ Add exponents for the product law; multiply only for power of a power.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Exponential form

Write products as powers.

Questions

Laws of exponents

Simplify using the laws.

Questions

Degree and unit digit

Find degrees and unit digits.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Form

Write 7 × 7 × 7 × 7 in exponential form.

▶ Show solution

7⁴.

Q2EASY· Product

Simplify 2³ × 2⁵.

▶ Show solution

2⁸ = 256.

Q3EASY· Quotient

Simplify 10⁶ ÷ 10².

▶ Show solution

10⁴ = 10000.

Q4EASY· Power of power

Simplify (3²)³.

▶ Show solution

3⁶ = 729.

Q5EASY· Zero exponent

Find 4⁰ + 5⁰.

▶ Show solution

1 + 1 = 2.

Q6MEDIUM· Degree / unit digit

State the degree of 6x⁵ − 2x³ + 9 and the unit digit of 2¹⁰.

▶ Show solution

Degree = 5; 2¹⁰ = 1024, unit digit 4.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 2 Chapter 3 of Samacheer Kalvi Class 7 Maths.
•aᵐ means a multiplied by itself m times; a⁰ = 1 for a ≠ 0.
•Product law: aᵐ × aⁿ = aᵐ⁺ⁿ.
•Quotient law: aᵐ ÷ aⁿ = aᵐ⁻ⁿ.
•Power of a power: (aᵐ)ⁿ = aᵐⁿ; same exponent: aᵐ × bᵐ = (ab)ᵐ.
•Degree = highest power of the variable; unit digits of powers repeat in cycles.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6-10 marks across exponent sums

Question type	Marks each	Typical count	What it tests
Objective	1	4-5	Single-law simplification
Multi-law	2	1-2	Combining laws
Degree / unit digit	2	1	Degree and pattern

Prep strategy

Decide which law applies before simplifying
Add for product, subtract for quotient, multiply for power of a power
Remember a⁰ = 1
Use cycles to find unit digits

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Large numbers

Exponents write huge numbers compactly (scientific notation).

Computing

Memory sizes are powers of 2.

Growth

Repeated doubling is modelled with powers.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Identify the law before applying it
Keep the base and combine exponents correctly
Use a⁰ = 1
Find unit digits using the repeating cycle

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Find the unit digit of 7¹⁰⁰ using its cycle.
Simplify (2² × 2³)² ÷ 2⁴.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 7 Term 2 ExamHigh

NMMS / Foundation MathsMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Because you are multiplying a by itself m times and then n more times, for a total of m + n times — so the exponents add.

Using the quotient law, aᵐ ÷ aᵐ = aᵐ⁻ᵐ = a⁰, and any non-zero number divided by itself is 1, so a⁰ = 1.

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