Exponents are just a shorthand for repeated multiplication — but Class 8 turns that shorthand into a small set of powerful rules. Multiply powers of the same base and you add the exponents; divide and you subtract; raise a power to a power and you multiply. Two ideas trip children up the most: that anything to the power zero is 1, and that a negative exponent means “one over” (so 4⁻² = 1/16, not −16). The chapter finishes with standard form — writing huge or tiny numbers as a digit times a power of ten.

This free printable worksheet has 12 questions from Bmathpro’s own question bank of 10,500+ validated maths questions — the same bank our enrolled students practise from. Every answer comes with a one-line explanation, so you can check your child’s method, not just the final answer.

Set aside 15–20 minutes, keep the answers hidden until the end, and let your child attempt every question — a wrong attempt tells you more than a skipped one.

What this worksheet covers

• Evaluating a power (like 3⁴)
• Multiplying and dividing powers of the same base (adding and subtracting exponents)
• Raising a power to a power (multiplying exponents)
• The zero exponent and negative exponents
• Combining several exponent laws in one expression
• Standard form (scientific notation) — reading it and writing it

Maps to the CBSE Class 8 Exponents and Powers chapter (NCERT) and equivalent ICSE/State-board units.

Class 8 Exponents and Powers Worksheet — 12 Questions

Warm-up

1. Evaluate: 3⁴. (Write your answer.)

2. Simplify: 2³ × 2⁴ = 2^? (give the exponent). (Write your answer.)

3. Evaluate: 5⁰. (Write your answer.)

4. Simplify: 2³ × 2².
A. 2¹  B. 2⁶  C. 2⁵  D. 4⁵

Building up

5. Simplify: 5⁸ ÷ 5¹ = 5^? (give the exponent). (Write your answer.)

6. Simplify: (3²)³ = 3^? (give the exponent). (Write your answer.)

7. Evaluate: 4⁻² (give your answer as a fraction). (Write your answer.)

8. Write 4.5 × 10⁴ as an ordinary number. (Write your answer.)

9. Write 5000 in scientific notation.
A. 50 × 10²  B. 5 × 10³  C. 0.5 × 10⁴  D. 5 × 10⁴

Challenge

10. Simplify (2³ × 2⁻¹) ÷ 2⁻² and give the value. (Write your answer.)

11. If 3ˣ = 81 and 2ʸ = 64, what is the value of x + y?
A. 12  B. 9  C. 10  D. 11

12. A sheet of paper is folded in half repeatedly. After each fold the number of layers doubles. How many layers are there after 7 folds? (Write your answer.)

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Answer key with explanations

Show answers and explanations (parents — open this after your child finishes)

1. 81 — 3 × 3 × 3 × 3 = 81.
2. 7 — multiplying same base adds exponents: 3 + 4 = 7.
3. 1 — any non-zero number to the power 0 equals 1.
4. C. 2⁵ — 2^(3+2) = 2⁵ = 32.
5. 7 — dividing same base subtracts exponents: 8 − 1 = 7.
6. 6 — power to a power multiplies exponents: 2 × 3 = 6.
7. 1/16 — 4⁻² = 1/4² = 1/16.
8. 45000 — 4.5 × 10⁴ = 45000.
9. B. 5 × 10³ — 5000 = 5 × 1000; front number between 1 and 10.
10. 16 — 2² ÷ 2⁻² = 2⁴ = 16.
11. C. 10 — 3⁴ = 81 (x = 4), 2⁶ = 64 (y = 6), x + y = 10.
12. 128 — 2⁷ = 128.

How to use this worksheet at home

• Keep it short and calm. 15–20 minutes beats an hour of pressure.
• Say the rule out loud. “Same base, multiplying — so I add the powers.” Naming it stops the add/multiply mix-up.
• Praise the method, not the marks. (We deliberately don’t put marks on our worksheets.)

FAQs

Is this worksheet free to print?
Yes — free to use and print at home, no sign-up needed.

Which syllabus does it follow?
Standard Class 8 Exponents and Powers chapter — CBSE (NCERT), ICSE and State boards.

Why does 4⁻² equal 1/16 and not −16?
A negative exponent never makes a number negative — it means “one over” the positive power. So 4⁻² = 1/4² = 1/16.

Where can my child get more practice like this?
Enrolled students get Math Gym, our paid practice app with 10,500+ questions — see our courses page.

Also practise: Class 8 Rational Numbers · Class 8 Linear Equations · all Class 8 worksheets.

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