positive coefficients, in multi-step
inequalities, 188
positive correlation, 336
positive number(s)
adding, 30-31
dividing, 40
dividing an inequality by, 180
multiplying, 38-39
multiplying an inequality by, 178-179
in nonlinear functions, 256
positive slope, 295
power(s). See also exponents
in algebraic expressions, 426
defined,^10
multiplying, 426, 433-436
with same base, 425-432
raising a power to, 433
raising a product to, 432, 435-437
raising a quotient to, 441
simplifying, 10, 419
PowerAlgebra.com, 2, 78, 162, 232,
292, 362, 416, 484, 544, 612, 662,
724
Powers of Powers and Powers of
Products, 432
Predict exercises, 341, 424, 432
Prime Numbers and Composite
Numbers, 798
prism, 147, 150, 502
probability
of compound events, 776-777,
779-780
defined, 769, 790
of dependent events, 778-789
of independent events, 777-778
of mutually exclusive events, 776-777
of overlapping events, 776-777
Probability, as Big Idea, 725, 785, 786
problem solving. See also problem-
solving strategies
Solve It!, 4, 10, 16, 23, 30, 38, 46, 53,
61, 81, 88 , 102, 109, 116, 124,
130, 137, 144, 164, 171, 178, 186,
194, 200, 207, 214, 234, 262, 268,
294, 301, 308, 315, 322, 330, 336,
346, 364, 372, 378, 387, 394, 400,
418, 425, 433, 439, 448, 453, 460,
467, 486, 492, 498, 504, 512, 518,
523, 529, 546, 553, 561, 568, 576,
582, 589, 596, 614, 619, 626, 633,
639, 645, 664, 670, 678, 684, 691,
698, 705, 726, 732, 738, 746, 753,
762, 769, 776
Think About a Plan exercises,^8 , 14,
21, 27, 35, 43, 51, 57, 65, 86 , 92,
99, 107, 113, 128, 135, 142, 149,
169, 176, 182, 190, 198, 205, 211,
219, 238, 244, 251, 258, 266, 272,
278, 299, 305, 313, 319, 326, 335,
342, 350, 368,
404, 422, 430,
465, 471,490,
521, 527, 532,
580, 587, 593,
637, 643, 650,
696, 703, 711,
757, 767, 773,376, 382, 391, 398,
437,443,451,458,
495, 502, 508, 516,
551, 557, 564, 571,
600, 617, 624, 630,
668 , 675, 682, 688 ,
730, 736, 743, 750,
781
problem-solving strategies
draw a diagram, 4, 5, 82, 138, 139,
216, 217, 219, 264, 495, 500, 502,
508, 564, 763
find a pattern, 6 , 8 , 43, 57, 65, 241,
248, 274, 275, 276, 278, 305, 422,
432, 454, 458, 624, 682
guess and check, 188, 324
make a chart, 12, 14, 62, 241, 247,
253, 255, 365, 458, 465, 499, 512,
551, 640, 641, 700, 701, 730, 733,
734
make an organized list, 512, 762
solve a simpler problem, 24, 27, 32,
94, 96, 116, 249, 420, 427, 430,
500, 505, 520, 620, 634
try, check, revise, 441
use logical reasoning, 437, 463, 671,
701, 708
work backward, 84, 202
write an equation, 57, 62, 95, 103,
107, 211, 242, 263, 388, 557, 578,
600, 621, 668 , 679, 688 , 772, 775,
779
products
cross, 125, 155, 220
of fractions, 804
of powers with same base, 425-426
radical expressions involving,
620, 627
simplifying, 435
Properties, as Big Idea, 3, 67, 68 , 417,
473, 474, 534, 535
Properties and Formulas, 816-819
property(ies)
Addition Property of Equality, 81, 153
Addition Property of Inequality, 171,
172
Associative Property of Addition, 23
Associative Property of Multiplication, 23
Commutative Property of Addition, 23
Commutative Property of
Multiplication, 23
Cross Products Property of a
Proportion, 125
Cumulative Property of Addition, 23
Cumulative Property of Multiplication,
23
Distributive Property, 46-47, 48, 49,
96, 188, 498
Dividing Powers With the Same Base,
439
Division Property of Equality, 83, 153Division Property of Exponents,
439-441
Division Property of Inequality, 180
Division Property of Square Roots,
621
and Formulas, 816-819
Identity Property of Addition, 24
Identity Property of Multiplication, 24
Inverse Property of Addition, 32
Inverse Property of Multiplication,
40-41
Multiplication Property, 124
Multiplication Property o f-1, 24
Multiplication Property of Equality, 83,
153
Multiplication Property of Exponents,
433-435
Multiplication Property of Inequality,
178, 179
Multiplication Property of Square
Roots, 619
Multiplying Powers With the Same
Base, 425
Raising a Power to a Power, 433
Raising a Product to a Power, 435
Raising a Quotient to a Power, 441
Reflexive Property of Equality, 184
Subtraction Property of Equality,
81, 153
Subtraction Property of Inequality, 173
Symmetric Property of Equality, 184
Transitive Property of Equality, 184
Transitive Property of Inequality, 184
Zero and Negative Exponents, 418
Zero-Product Property, 568
Zero Property of Multiplication, 24
Proportionality, as Big Idea, 79, 151,
152, 293, 352, 353
proportions
defined, 124
involving radicals, 628
multi-step, 126
percent, 137
rational, 694
in similar figures, 130
solving, 124-129, 694
solving using Cross Products Property,
125
solving using Multiplication Property,
124
using to find side lengths, 131
using to interpret scale drawings, 132
using to solve problems, 126
Pull It All Together, 67, 151, 221, 282,
352, 407, 473, 534, 602, 652, 714,
785
Pythagorean Theorem
converse of, 616
defined, 614, 654
using, 614-615C
Po w erAlg eb ra.com [in d e x —^937