📘 Class 8 Maths – Chapter 12
Exponents & Powers – Step 3 Notes
🔹 1. What are Exponents?
When a number is multiplied by itself repeatedly, we write it in exponential form.
Example: 5 × 5 × 5 = 5³
- 5 → Base
- 3 → Exponent (Power)
🔹 2. Laws of Exponents
Law 1: Same base, add powers
am × an = am+n
Example: 2³ × 2⁴ = 2⁷
Law 2: Same base, subtract powers
am ÷ an = am−n (a ≠ 0)
Example: 5⁶ ÷ 5² = 5⁴
Law 3: Power of a power
(am)n = am×n
Example: (3²)⁴ = 3⁸
Law 4: Power of a product
(ab)m = am × bm
Law 5: Power of a quotient
(a/b)m = am / bm, b ≠ 0
🔹 3. Zero Exponent
Any non-zero number raised to the power 0 is 1.
a0 = 1
Example: 7⁰ = 1
🔹 4. Negative Exponents
A negative exponent means reciprocal.
a−m = 1 / am
Example: 2−3 = 1 / 8
🔹 5. Standard Form
A number written as:
a × 10n
Where 1 ≤ a < 10
Example: 350000 = 3.5 × 10⁵
🧠Easy Memory Tricks
- Multiply → Add powers
- Divide → Subtract powers
- Power on power → Multiply powers
- Negative power → Flip the fraction
⭐ CBSE Exam Tips
- Write steps clearly
- Mention law used
- Avoid skipping simplification
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