Laws of exponents: Class 8 practice

What you should know first

• Multiplication of integers

The idea behind laws of exponents

For the same base: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, and a⁻ⁿ = 1/aⁿ.

Step-by-step method

1. Make sure the bases are the same.
2. Add powers when multiplying, subtract when dividing.
3. Multiply powers for a power of a power.
4. Turn negative powers into reciprocals.

Worked example 1 (Basic)

Simplify 2^3 × 2^1 ÷ 2^2 and find its value.

1. Add powers: 2^4
2. Subtract: 2^4 ÷ 2^2 = 2^2
3. Value = 4
4. Answer: 2^2 = 4

Worked example 2 (Standard)

Simplify (3^4)^3 ÷ 3^10.

1. (3^4)^3 = 3^12
2. 3^12 ÷ 3^10 = 3^2
3. Answer: 3² = 9

Worked example 3 (Challenge)

Simplify 5^2 × 5^4 ÷ 5^7 and find its value.

1. Add powers: 5^6
2. Subtract: 5^6 ÷ 5^7 = 5^-1
3. Value = 1/5
4. Answer: 5^-1 = 1/5

Common mistakes and misconceptions

• Multiplying powers when multiplying (2³ × 2² ≠ 2⁶)
• Thinking a⁻² is negative

Practice questions

1. (Basic) Simplify 5^3 × 5^2 ÷ 5^2 and find its value.
2. (Basic) Simplify 5^6 × 5^5 ÷ 5^4 and find its value.
3. (Standard) Simplify (3^6)^2 ÷ 3^10.
4. (Standard) Simplify (3^4)^2 ÷ 3^6.
5. (Challenge) Simplify 5^2 × 5^3 ÷ 5^7 and find its value.
6. (Challenge) Simplify 5^3 × 5^5 ÷ 5^9 and find its value.

Answer key with full working

• Q1: Add powers: 5^5 → Subtract: 5^5 ÷ 5^2 = 5^3 → Value = 125 → Answer: 5^3 = 125
• Q2: Add powers: 5^11 → Subtract: 5^11 ÷ 5^4 = 5^7 → Value = 78125 → Answer: 5^7 = 78125
• Q3: (3^6)^2 = 3^12 → 3^12 ÷ 3^10 = 3^2 → Answer: 3² = 9
• Q4: (3^4)^2 = 3^8 → 3^8 ÷ 3^6 = 3^2 → Answer: 3² = 9
• Q5: Add powers: 5^5 → Subtract: 5^5 ÷ 5^7 = 5^-2 → Value = 1/25 → Answer: 5^-2 = 1/25
• Q6: Add powers: 5^8 → Subtract: 5^8 ÷ 5^9 = 5^-1 → Value = 1/5 → Answer: 5^-1 = 1/5

Syllabus note

This skill is listed under "Exponents and Powers" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

• Exponents and Powers chapter notes (Class 8)
• Negative exponents and very small numbers
• Linear equations with the variable on both sides
• Square roots by prime factorisation
• Compound interest calculations
• Inverse proportion problems
• All Class 8 practice

Frequently asked questions

Which chapter is laws of exponents in?

"Exponents and Powers", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.