Students are able to use exponent rules to simplify expressions.pptx

Laws of Exponents – Description The laws of exponents are a set of rules that define how to perform operations involving powers or exponents. These laws simplify expressions where the same base is raised to different powers and are fundamental in algebra and higher-level math. Understanding these rules helps in simplifying complex expressions and solving equations efficiently. The main laws of exponents include: Product of Powers Rule: 𝑎 𝑚 ⋅ 𝑎 𝑛 = 𝑎 𝑚 + 𝑛 a m ⋅a n =a m+n (Add the exponents when multiplying like bases) Quotient of Powers Rule: 𝑎 𝑚 𝑎 𝑛 = 𝑎 𝑚 − 𝑛 a n a m ​ =a m−n (Subtract the exponents when dividing like bases) Power of a Power Rule: ( 𝑎 𝑚 ) 𝑛 = 𝑎 𝑚 𝑛 (a m ) n =a mn (Multiply the exponents) Power of a Product Rule: ( 𝑎 𝑏 ) 𝑛 = 𝑎 𝑛 ⋅ 𝑏 𝑛 (ab) n =a n ⋅b n (Distribute the exponent to each base in the product) Power of a Quotient Rule: ( 𝑎 𝑏 ) 𝑛 = 𝑎 𝑛 𝑏 𝑛 ( b a ​ ) n = b n a n ​ (Distribute the exponent to both numerator and denominator) Zero Exponent Rule: 𝑎 0 = 1 a 0 =1 (for any 𝑎 ≠ 0 a  =0) (Any non-zero number raised to the power of zero is 1) Negative Exponent Rule: 𝑎 − 𝑛 = 1 𝑎 𝑛 a −n = a n 1 ​ (A negative exponent means take the reciprocal)