# Algebra 2

The function transformation project.

The Product and Quotient Properties of Radicals

Product Property of Radicals

(square root)ab = (square root)a times (square root)b

Eg.1: (square root)9 times 3 = 9square root)9 times (square root)3 = 3(square root)6

Eg.2: (square root)54 = (square root)9 times 6 = (square root)9 times (square root)6 = 3(square root)6

Eg.3: (square root)300 = (square root)100 times 3 + (square root)100 times (square root)3 = 10(square root)3

Eg.4: (square root)75 = (square root)25 times3 = (square root)25 times (square root)3 = 5(square root)3

Quotient Properties of Radicals

(square root)a/b = (square root)a/(square root)b

Eg.1 (square root)36/25 = (square root)36/(square root)25 = 6/5

Eg.2 (square root)3/16 = (square root)3/(square root)16 = 9square root)3/4

Rationalizing The Denominator

Eg.1 (square root)2/(square root)7 = (square root)2 times (square root)7/(square root)7 times (square root)7 = (square root)14/(square root)49 = (square root)14/7

Eg.2 (square root)25/8 = (square root)4 times 6/8 = (square root)4 times (square root)6/8 = 2(square root) 6/8 = (square root)6/4

Eg.3 9+3(square root)2/6 = 9/6 + 3(square root)2/6 =3/2 + 1(square root)2/2 = 3+(square root)2/2

Eg/4 10-(square root)50/20 = 10-9square root)25 times 2/20 = 10-5(square root)2/20 = 10/20 – 59square root)2/20 = 1/2 – 19square root)2/4 = 1/2-(square root)2/4

Zero and the Negative Exponent Properties

Zero Exponent Property = Any quantity raised to the zero power equals to 1/ m to the 0 power = 1

Negative Exponent Property = a to the negative power = the reciprocal of a to the n

a to the negative power = 1/a to the n

2 to the negative 3 = 1/2 to the third

Properties of Exponents

The Product Rule: a to m times a to n = a to m + n

The Quotient Rule: a to m/ a to n = a to m-n

The Power Rule: (a to m)to n = a to m times n

Product to a power: (ab)to n = a to n times b to n

Quotient to a power = (a/b)to n = an/bn

Other Properties:

a to 1 = a

a to u = 1

Relations and Functions

Domain and Range

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