Page 900 - Algebra 1

Inverse Property of Multiplication
(11)
For every real number _a , where a ≠ 0 and b ≠ 0,
Power of a Product Property
(4 0)
If x and y are any nonzero real numbers and m is an integer, then (xy)m = xmym.
Power of a Quotient Property
(4 0)
_a · _b = 1. ba
b
Multiplication Property of Equality
(21)
For every real number a, b, and c, if a = b, then ac = bc.
Multiplication Property of Inequality
(70)
For every real number a, b, and c, where c > 0, if a < b, then ac < bc.
For every real number a, b, and c, where c < 0, if a < b, then ac > bc.
Also holds true for >, ≤, ≥, and ≠. Multiplication Property of Zero
(11)
For every real number a, a · 0 = 0. Multiplication Property of -1
(11)
For every real number a, -1 · a = -a. Negative Exponent Property
(32)
For any nonzero real number x and integer n, x-n=_1and_1 =xn.
Order of Operations
(4)
To evaluate expressions:
1. Work inside grouping symbols.
2. Simplify powers and roots.
3. Multiply and divide from left to right. 4. Add and subtract from left to right.
Power of a Power Property
(4 0)
If x is any nonzero real number and m and n are integers, then (xm)n = xmn.
If x and y are any nonzero real numbers and m is an integer, then _x m = _xm .
(y) ym
Product Property of Exponents
xn x-n
(3)
If x is any nonzero real number and m and n are integers, then xm · xn = xm+n.
Product Property of Radicals
(61)
If m and n are non negative real numbers, then √m √n = √m n and √m n = √m √n .
Pythagorean Theorem
(85)
If a triangle is a right triangle with legs of lengths a and b and hypotenuse of length c, then
a2 +b2 =c2.
Quotient Property of Exponents
(32)
If x is any nonzero real number and m and n are integers, then _xm = xm-n.
xn
Quotient Property of Radicals
(103)
If m ≥ 0 and n > 0, then Scientific Notation
(37)
A number written as a × 10n, where 1 ≤ a < 10 and n is an integer.
Subtraction Property of Equality
(19)
For every real number a, b, and c, if a = b, then a - c = b - c.
m = √m . ____
√m = √n
m and √n
√n
√n
Properties and Formulas 885
PROPERTIES AND FORMULAS