Properties and Rules for Exponents Properties and Rules for Radicals radicand Exponents and Radicals base Properties and Rules for Exponents Product Rule Quotient Power Zero Exponent Negative Exponent Power of a quotient Bases are different Bases are the same Properties and Rules for Radicals Principal square root of a Negative Cube root of a nth root of a nth root of an if n is an even and positive integer if n is an odd and positive integer Product Rule for Radicals Quotient Rule Like radicals Conjugates a ≥0 Connections (7.2) n is the root or index m is the power or exponent

Rational Exponents Write with exponent notation Write with radical notation Simplify if possible

Rational Exponents Write with exponent notation Write with radical notation Simplify if possible

Rational Exponents Write with exponent notation Write with radical notation Simplify if possible

Rational Exponents Things to remember: Always write final answer with positive exponents When using a combination of rules to simplify a problem, there are usually various ways to get the final answer. What is important is that you know and understand each rule individually!

Rational Exponents Things to remember: Always write final answer with positive exponents When using a combination of rules to simplify a problem, there are usually various ways to get the final answer. What is important is that you know and understand each rule individually!

Simplifying using exponent notation Rewrite with exponent notation and simplify Write final answer using radical notation Can we write 9 as a power? The root for both is still the same

Using exponent notation to write as a single radical (same root) Rewrite with exponent notation Write exponents with the same common denominator (this will be the root of the radical) Write final answer using radical notation and simplify if possible Root is 6 LCD is 6 LCD is 12 Root is 12 LCD is 10 Root is 10