Understanding the Laws of Exponents

Laws Of Exponents

When numbers have exponents and you need to combine them, there are simple rules to follow. Think of these laws as math "shortcuts" that save you time and effort!

The first law tells us that when multiplying expressions with the same base, you add the exponents $3² · 3⁵ = 3²⁺⁵ = 3⁷$. For division with the same base, subtract the exponents $3⁵ ÷ 3² = 3⁵⁻² = 3³$.

When raising a power to another power, you multiply the exponents $like (3²)⁵ = 3²·⁵ = 3¹⁰$. With expressions like (3·4)², you can split it into 3² · 4². For fractions, the rule is similar: (³⁄₄)² = ³²/₄² = ⁹⁄₁₆.

Remember This! Negative exponents flip the fraction! When you see (³⁄₄)⁻² it equals (⁴⁄₃)², and ³⁻²/₄⁻⁵ equals ₄⁵/₃². This rule trips up many students, so practice it extra!