The Five Essential Index Laws
Multiplication Law is your first power tool - when multiplying numbers with the same base, simply add the exponents together. For example, x³ × x⁵ = x⁸ because 3 + 5 = 8.
Division Law works in reverse - when dividing powers with the same base, subtract the exponents. So x⁷ ÷ x³ = x⁴ because 7 - 3 = 4.
The Power of a Power Law handles nested exponents by multiplying them together. When you see (x²)³, you get x⁶ because 2 × 3 = 6.
Zero Index Law might seem odd, but any number to the power of zero always equals 1. Whether it's 5⁰ or 999⁰, the answer is always 1.
Negative Index Law turns negative exponents into fractions. x⁻³ becomes 1/x³, so 4⁻³ equals 1/64.
Quick Tip: Remember the pattern - multiplication adds, division subtracts, powers multiply, zero gives one, and negatives flip to fractions!