How to Multiply Numbers with Different Bases and the Same Exponent

The Rule for Multiplying Numbers with Same Exponents

• 💡 The core principle is that when multiplying numbers with different bases but the same exponent, you can multiply the bases together and keep the exponent the same.
• 🔑 This is represented by the formula: X^A * Y^A = (X * Y)^A.

Applying the Formula

• 🎯 For example, 3^2 * 4^2 simplifies to (3 * 4)^2, which equals 12^2.
• 🚀 Similarly, 2^5 * 3^5 becomes (2 * 3)^5, resulting in 6^5.
• 📈 Another example, 6^4 * 5^4 is calculated as (6 * 5)^4, yielding 30^4.

Understanding the Concept

• 🧠 The exponent remains unchanged because it applies to the result of the base multiplication.
• ✅ When exponents are 1, like in 3 * 4 = 12, the exponent stays 1, illustrating the same principle.
• 🌟 This rule holds true regardless of the specific exponent value, as shown with 5^3 * 4^3 becoming 20^3.