 P.2.1: In the exponential form an, n is the _______ and a is the _______ .
 P.2.2: One of the two equal factors of a number is called a _______ of the...
 P.2.3: The _______ of a number a is the nth root that has the same sign as a
 P.2.4: In the radical form n a, the positive integer n is called the _____...
 P.2.5: Creating a radicalfree denominator is known as _______ the denomin...
 P.2.6: In the expression bmn, m denotes the _______ to which the base is r...
 P.2.7: What is the conjugate of 2 + 35?
 P.2.8: When is an expression involving radicals in simplest form?
 P.2.9: . Is 10.678 103 written in scientific notation?
 P.2.10: Is 64 a perfect square, a perfect cube, or both?
 P.2.11: In Exercises 1118, evaluate each expression. (a) 3 33
 P.2.12: In Exercises 1118, evaluate each expression. a) 53 52 (b) 42 4
 P.2.13: In Exercises 1118, evaluate each expression. (a) (43)0 (b) 6 63
 P.2.14: In Exercises 1118, evaluate each expression. (a) 24(2)5 (b) 70
 P.2.15: In Exercises 1118, evaluate each expression. (a) 24(2)5 (b) 70
 P.2.16: In Exercises 1118, evaluate each expression. . (a) (23 32)2 (b) (58)2
 P.2.17: In Exercises 1118, evaluate each expression. (a) 21 + 31 (b) (31)3
 P.2.18: In Exercises 1118, evaluate each expression. a) 4 32 22 31 (b) 31 + 22
 P.2.19: In Exercises 1924, evaluate the expression for the value of x. 2x3,...
 P.2.20: In Exercises 1924, evaluate the expression for the value of x. 3x4,...
 P.2.21: In Exercises 1924, evaluate the expression for the value of x. 5(x)...
 P.2.22: In Exercises 1924, evaluate the expression for the value of x. 6x0 ...
 P.2.23: In Exercises 1924, evaluate the expression for the value of x. 7x2,...
 P.2.24: In Exercises 1924, evaluate the expression for the value of x. 20x2...
 P.2.25: In Exercises 2532, simplify each expression. . (a) x3(x2) (b) x4(3x5
 P.2.26: In Exercises 2532, simplify each expression. (a) 4z4(2z3) (b) 5x3(4x2)
 P.2.27: In Exercises 2532, simplify each expression. (a) (3x)2 (b) (4x3)0, x 0
 P.2.28: In Exercises 2532, simplify each expression. (a) 6z2(2z5)4 (b) (3x5...
 P.2.29: In Exercises 2532, simplify each expression. (a) 7x2 x3 (b) 12(x + ...
 P.2.30: In Exercises 2532, simplify each expression. a) r5 r9 (b) 3x2y4 15(...
 P.2.31: In Exercises 2532, simplify each expression. (a) [(x2y2)1]1 (b) (a2...
 P.2.32: In Exercises 2532, simplify each expression. a) (4y)3(3y)4(b) (5x2z...
 P.2.33: In Exercises 3338, use a calculator to evaluate the expression. (Ro...
 P.2.34: In Exercises 3338, use a calculator to evaluate the expression. (Ro...
 P.2.35: In Exercises 3338, use a calculator to evaluate the expression. (Ro...
 P.2.36: In Exercises 3338, use a calculator to evaluate the expression. (Ro...
 P.2.37: In Exercises 3338, use a calculator to evaluate the expression. (Ro...
 P.2.38: In Exercises 3338, use a calculator to evaluate the expression. (Ro...
 P.2.39: In Exercises 3952, write the number in scientific notation. 973.50
 P.2.40: In Exercises 3952, write the number in scientific notation. 28,022.2
 P.2.41: In Exercises 3952, write the number in scientific notation. 10,252.484
 P.2.42: In Exercises 3952, write the number in scientific notation. 525,252...
 P.2.43: In Exercises 3952, write the number in scientific notation. . 1110.25
 P.2.44: In Exercises 3952, write the number in scientific notation. 5,222,145
 P.2.45: In Exercises 3952, write the number in scientific notation. 0.0002485
 P.2.46: In Exercises 3952, write the number in scientific notation. 0.0000025
 P.2.47: In Exercises 3952, write the number in scientific notation. 0.0000025
 P.2.48: In Exercises 3952, write the number in scientific notation. 0.00012...
 P.2.49: In Exercises 3952, write the number in scientific notation. Land ar...
 P.2.50: In Exercises 3952, write the number in scientific notation. Light y...
 P.2.51: In Exercises 3952, write the number in scientific notation. Relativ...
 P.2.52: In Exercises 3952, write the number in scientific notation. One mic...
 P.2.53: In Exercises 5360, write the number in decimal notation. 1.08 104
 P.2.54: In Exercises 5360, write the number in decimal notation. 4.816 108
 P.2.55: In Exercises 5360, write the number in decimal notation. 7.65 107
 P.2.56: In Exercises 5360, write the number in decimal notation. 5.098 1010
 P.2.57: In Exercises 5360, write the number in decimal notation. Mean SAT M...
 P.2.58: In Exercises 5360, write the number in decimal notation. Core tempe...
 P.2.59: In Exercises 5360, write the number in decimal notation. Width of a...
 P.2.60: In Exercises 5360, write the number in decimal notation. Charge of ...
 P.2.61: In Exercises 6166, evaluate the expression without using a calculator.
 P.2.62: In Exercises 6166, evaluate the expression without using a calculator.
 P.2.63: In Exercises 6166, evaluate the expression without using a calculator.
 P.2.64: In Exercises 6166, evaluate the expression without using a calculator.
 P.2.65: In Exercises 6166, evaluate the expression without using a calculator.
 P.2.66: In Exercises 6166, evaluate the expression without using a calculator.
 P.2.67: In Exercises 6770, use a calculator to evaluate each expression. (R...
 P.2.68: In Exercises 6770, use a calculator to evaluate each expression. (R...
 P.2.69: In Exercises 6770, use a calculator to evaluate each expression. (R...
 P.2.70: In Exercises 6770, use a calculator to evaluate each expression. (R...
 P.2.71: In Exercises 7178, evaluate the expression (if possible) without us...
 P.2.72: In Exercises 7178, evaluate the expression (if possible) without us...
 P.2.73: In Exercises 7178, evaluate the expression (if possible) without us...
 P.2.74: In Exercises 7178, evaluate the expression (if possible) without us...
 P.2.75: In Exerises 7178, evaluate the expression (if possible) without usi...
 P.2.76: In Exercises 7178, evaluate the expression (if possible) without us...
 P.2.77: In Exercises 7178, evaluate the expression (if possible) without us...
 P.2.78: In Exercises 7178, evaluate the expression (if possible) without us...
 P.2.79: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.80: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.81: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.82: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.83: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.84: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.85: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.86: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.87: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.88: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.89: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.90: In Exercises 7990, use a calculator to approximate the value of the...
 P.2.91: In Exercises 9194, use the properties of radicals to simplify each ...
 P.2.92: In Exercises 9194, use the properties of radicals to simplify each ...
 P.2.93: In Exercises 9194, use the properties of radicals to simplify each ...
 P.2.94: In Exercises 9194, use the properties of radicals to simplify each ...
 P.2.95: In Exercises 95102, simplify each expression. . (a) 45 (b) 3 32a2b2
 P.2.96: In Exercises 95102, simplify each expression. (a) 3 54 (b) 32x3y4
 P.2.97: In Exercises 95102, simplify each expression. (a) 3 16x5 (b) 75x2y4
 P.2.98: In Exercises 95102, simplify each expression. (a) 4 3x4y2 (b) 5 160...
 P.2.99: In Exercises 95102, simplify each expression. (a) 250 + 128 (b) 103...
 P.2.100: In Exercises 95102, simplify each expression. . (a) 5x 3x (b) 29y + 0y
 P.2.101: In Exercises 95102, simplify each expression. (a) 3x + 1 + 10x + 1 ...
 P.2.102: In Exercises 95102, simplify each expression. (a) 510x2 90x2 (b) 8 ...
 P.2.103: In Exercises 103106, complete the statement with <, =, or > 3 11311
 P.2.104: In Exercises 103106, complete the statement with <, =, or > 5 + 35 + 3
 P.2.105: In Exercises 103106, complete the statement with <, =, or > . 532 + 22
 P.2.106: In Exercises 103106, complete the statement with <, =, or > 532 + 4
 P.2.107: In Exercises 107110, rationalize the denominator of the expression....
 P.2.108: In Exercises 107110, rationalize the denominator of the expression....
 P.2.109: In Exercises 107110, rationalize the denominator of the expression....
 P.2.110: In Exercises 107110, rationalize the denominator of the expression....
 P.2.111: In Exercises 111114, rationalize the numerator of the expression. T...
 P.2.112: In Exercises 111114, rationalize the numerator of the expression. T...
 P.2.113: In Exercises 111114, rationalize the numerator of the expression. T...
 P.2.114: In Exercises 111114, rationalize the numerator of the expression. T...
 P.2.115: In Exercises 115 and 116, reduce the index of each radical and rewr...
 P.2.116: In Exercises 115 and 116, reduce the index of each radical and rewr...
 P.2.117: In Exercises 117124, fill in the missing form of the expression. 364
 P.2.118: In Exercises 117124, fill in the missing form of the expression. 144
 P.2.119: In Exercises 117124, fill in the missing form of the expression. 1/32
 P.2.120: In Exercises 117124, fill in the missing form of the expression. 316
 P.2.121: In Exercises 117124, fill in the missing form of the expression. (243
 P.2.122: In Exercises 117124, fill in the missing form of the expression. 34...
 P.2.123: In Exercises 117124, fill in the missing form of the expression. 34...
 P.2.124: In Exercises 117124, fill in the missing form of the expression. 1654
 P.2.125: In Exercises 125132, simplify the expression. 2x2)32 212x4
 P.2.126: In Exercises 125132, simplify the expression. x43y23 (xy)13
 P.2.127: In Exercises 125132, simplify the expression. x43y23 (xy)13
 P.2.128: In Exercises 125132, simplify the expression. 512 5x52 (5x)32
 P.2.129: In Exercises 125132, simplify the expression. 235
 P.2.130: In Exercises 125132, simplify the expression. 9 4) 1
 P.2.131: In Exercises 125132, simplify the expression. ( 1 27) 1
 P.2.132: In Exercises 125132, simplify the expression. ( 1 125) 4
 P.2.133: In Exercises 133136, write each expression as a single radical. The...
 P.2.134: In Exercises 133136, write each expression as a single radical. The...
 P.2.135: In Exercises 133136, write each expression as a single radical. The...
 P.2.136: In Exercises 133136, write each expression as a single radical. The...
 P.2.137: The table shows the 2013 estimated populations and gross domestic p...
 P.2.138: There were 2.51 108 tons of municipal waste generated in 2012. Find...
 P.2.139: A funnel is filled with hydrochloric acid to a height of h centimet...
 P.2.140: In Exercises 140143, determine whether the statement is true or fal...
 P.2.141: In Exercises 140143, determine whether the statement is true or fal...
 P.2.142: In Exercises 140143, determine whether the statement is true or fal...
 P.2.143: In Exercises 140143, determine whether the statement is true or fal...
 P.2.144: Package A is a cube with a volume of 500 cubic inches. Package B is...
 P.2.145: Verify that a0 = 1, a 0. (Hint: Use the property of exponents aman ...
 P.2.146: List all possible digits that occur in the units place of the squar...
 P.2.147: Square the real number 53 and note that the radical is eliminated f...
Solutions for Chapter P.2: Prerequisites
Full solutions for Algebra and Trigonometry: Real Mathematics, Real People  7th Edition
ISBN: 9781305071735
Solutions for Chapter P.2: Prerequisites
Get Full SolutionsSince 147 problems in chapter P.2: Prerequisites have been answered, more than 51652 students have viewed full stepbystep solutions from this chapter. Chapter P.2: Prerequisites includes 147 full stepbystep solutions. Algebra and Trigonometry: Real Mathematics, Real People was written by and is associated to the ISBN: 9781305071735. This textbook survival guide was created for the textbook: Algebra and Trigonometry: Real Mathematics, Real People, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Iterative method.
A sequence of steps intended to approach the desired solution.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.