Multiplication and division with exponents

Key Notes :

🌟 Multiplication and Division with Exponents 🌟

✳️ What are Exponents?

An exponent tells how many times a number (called the base) is multiplied by itself.

• 👉 Example: 2⁴=2×2×2×2=16

Here, 2 is the base and 4 is the exponent.

✴️ Multiplying Powers with the Same Base

When bases are the same, add the exponents.

a^m×aⁿ=a^m+n

👉 Example: 3²×3⁴=3²⁺⁴=3⁶=729

🧠 Remember: Base must be the same!

✳️ Dividing Powers with the Same Base

When bases are the same, subtract the exponents.

a^m/aⁿ=a^m−n

👉 Example: 5⁷÷5³=5⁷⁻³=5⁴=625

✴️ Power of a Power Rule

When you raise a power to another power, multiply the exponents.

(a^m)ⁿ=a^m×n

👉 Example: (2³)⁴=2^3×4=2¹²

✳️ Power of a Product Rule

When multiplying two bases with an exponent outside, apply the exponent to each base.

(ab)^m=a^m×b^m

👉 Example: (2×3)²=2²×3²=4×9=36

✴️ Power of a Quotient Rule

When dividing two bases with an exponent outside, apply the exponent to both numerator and denominator.

(a/b)^m=a^m/b^m

👉 Example: (4/2)³=4³/2³=64/8=8

✳️ Zero and Negative Exponents

• Zero Exponent Rule: a0=1(a≠0)
• Negative Exponent Rule: a⁻ⁿ=1/aⁿ

👉 Example: 2⁻³=1/2³=1/8

💡 Quick Tips to Remember

✅ Same base → Add or subtract exponents (depending on × or ÷).

✅ Different base → Apply exponent separately.

✅ Power to power → Multiply exponents.

✅ Always simplify at the end!

🧮 Practice Examples

1️⃣ 6³×6²=6⁵=7776

2️⃣ 8⁵÷8³=8²=64

3️⃣ (3²)³=3⁶=729

4️⃣ (2×5)²=2²×5²=100

🎯 Summary Chart

Operation	Rule	Example
Multiply powers	am×an=am+n	23×24=27
Divide powers	am÷an=am−n	56÷52=54
Power of a power	(am)n=am×n	(32)3=36
Power of a product	(ab)m=am×bm	(2×3)2=22×32
Power of a quotient	(a/b)m=am/bm	(4/2)3=64/8

Learn with an example

Let’s practice!🖊️