Radical and Rational Exponents

SAT Math · Axiom Academy

Simplify, Solve, and Convert Between Forms Understanding Radicals & Exponents Radicals and exponents are two ways to express the same mathematical idea. means "what number squared equals 9?" Answer: 3 means "what number cubed equals 8?" Answer: 2 means "what number to the 4th equals 16?" Answer: 2 Simplifying Radical Expressions Rule 1: Extract Perfect Powers If any factor under the radical is a perfect power, pull it out. Rule 4: Rationalize the Denominator Don't leave radicals in the denominator! Multiply by a form of 1. Isolate the radical expression on one side Raise both sides to the power of the radical's index CHECK: Substitute back—radical equations can introduce extraneous solutions! Fluently switch between radical and exponential notation. Sometimes it's easier to work with exponents. For example:

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