Algebra II 6.5-6.6

Product of powers

a^m x aⁿ = a^m+n .

Quotient of Powers

a^m / aⁿ = a^m-n .

Power of powers

(a^m )ⁿ = a^mn .

Power of product

(ab)^m = a^m b^m .

Negative exponents

a^-m = 1/a^m .

Simplest form of radicals

N is as SMALL AS POSSIBLE

Radicand contains NO FACTORS (other than 1) which is nth powers of interger/ polynomials

Radicand contains NO FRACTIONS

NO RADICALS IN DENOMINATOR

add or subtract

To ____ or _________ radicals; THEY MUST BE LIKE RADICALS

**INDEX AND RADICAL ARE THE SAME

Product property

nth root of a PRODUCT OF NONNEGATIVE real numbers is EQUAL to the product of the nth root of thos numbers

EX: ⁿ√a x ⁿ√b = ⁿ√ab

same index

you can ONLY MULTIPLY radicals together if they have the _____ _______ (root)

Quotient property

nth root of a quotient of nonnegative real number is EQUAL to the quotient of the nth root of those numbers

rationalize denominator

Used to ELIMINATE RADICALS FROM DENOMINATOR

Multiply the Numerator and Denominator by QUANTITY so the RADICAND has an EXACT ROOT

Rationalize using conjugates

Multiple numerator AND denominator by the CONJUGATE DENOMINATOR

**ONLY THING THAT CHANGES IS SIGN INBETWEEN RADICAL AND CONSTANT

Solving radical

Isolate each radical

Raise EACH SIDE of equation to POWER EQUAL TO INDEX of radical (eliminates the radical)

SOLVE RESULTING Equation