 P.2.1: Evaluate each exponen#al expression in rerd5es 122. 52 2
 P.2.2: Evaluate each exponen#al expression in rerd5es 122. 62 2
 P.2.3: Evaluate each exponen#al expression in rerd5es 122. ( 2}'
 P.2.4: Evaluate each exponen#al expression in rerd5es 122. ( 2)'
 P.2.5: Evaluate each exponen#al expression in rerd5es 122.  2'
 P.2.6: Evaluate each exponen#al expression in rerd5es 122.  2'
 P.2.7: Evaluate each exponen#al expression in rerd5es 122. ( 3)0
 P.2.8: Evaluate each exponen#al expression in rerd5es 122. ( 9)"
 P.2.9: Evaluate each exponen#al expression in rerd5es 122.  3
 P.2.10: Evaluate each exponen#al expression in rerd5es 122.  </'
 P.2.11: Evaluate each exponen#al expression in rerd5es 122. 4.1
 P.2.12: Evaluate each exponen#al expression in rerd5es 122. 2"6
 P.2.13: Evaluate each exponen#al expression in rerd5es 122. 22 . 23
 P.2.14: Evaluate each exponen#al expression in rerd5es 122. 33 32
 P.2.15: Evaluate each exponen#al expression in rerd5es 122. (22)3
 P.2.16: Evaluate each exponen#al expression in rerd5es 122. (33)2
 P.2.17: Evaluate each exponen#al expression in rerd5es 122. 2'2'
 P.2.18: Evaluate each exponen#al expression in rerd5es 122. 3s3'
 P.2.19: Evaluate each exponen#al expression in rerd5es 122. 3 3 3
 P.2.20: Evaluate each exponen#al expression in rerd5es 122. 2"3 2
 P.2.21: Evaluate each exponen#al expression in rerd5es 122. 2' 3'2'
 P.2.22: Evaluate each exponen#al expression in rerd5es 122. 3'2' z;
 P.2.23: Simplify each exponential expression in Exercises 2364. x 2y
 P.2.24: Simplify each exponential expression in Exercises 2364. xy3
 P.2.25: Simplify each exponential expression in Exercises 2364. xy'
 P.2.26: Simplify each exponential expression in Exercises 2364. \'7)'0
 P.2.27: Simplify each exponential expression in Exercises 2364. x' x1
 P.2.28: Simplify each exponential expression in Exercises 2364. x" .. r'
 P.2.29: Simplify each exponential expression in Exercises 2364. x5 x 10
 P.2.30: Simplify each exponential expression in Exercises 2364. x6 x11
 P.2.31: Simplify each exponential expression in Exercises 2364. (.r'J'
 P.2.32: Simplify each exponential expression in Exercises 2364. x 11 )5
 P.2.33: Simplify each exponential expression in Exercises 2364. (,r')3
 P.2.34: Simplify each exponential expression in Exercises 2364. (.r'J'
 P.2.35: Simplify each exponential expression in Exercises 2364. " x"' ~
 P.2.36: Simplify each exponential expression in Exercises 2364. x"' ~ To x1 X
 P.2.37: Simplify each exponential expression in Exercises 2364. xu x"' :;...
 P.2.38: Simplify each exponential expression in Exercises 2364. x"' :; . ...
 P.2.39: Simplify each exponential expression in Exercises 2364. (&r')2
 P.2.40: Simplify each exponential expression in Exercises 2364. (6x'f 2
 P.2.41: Simplify each exponential expression in Exercises 2364. ;)'
 P.2.42: Simplify each exponential expression in Exercises 2364. :v 6)
 P.2.43: Simplify each exponential expression in Exercises 2364. 11ryr
 P.2.44: Simplify each exponential expression in Exercises 2364. ( 1r'y')3
 P.2.45: Simplify each exponential expression in Exercises 2364. (3x')(2r7)
 P.2.46: Simplify each exponential expression in Exercises 2364. (11 .r')(9...
 P.2.47: Simplify each exponential expression in Exercises 2364. ( 9.r1y)(...
 P.2.48: Simplify each exponential expression in Exercises 2364. ( 5x'y)(...
 P.2.49: Simplify each exponential expression in Exercises 2364. 8x'" 2Qrl4...
 P.2.50: Simplify each exponential expression in Exercises 2364. 2Qrl4  2...
 P.2.51: Simplify each exponential expression in Exercises 2364. 25a13b. 3S...
 P.2.52: Simplify each exponential expression in Exercises 2364. 3Sa"b'St. ...
 P.2.53: Simplify each exponential expression in Exercises 2364. 14b77b"
 P.2.54: Simplify each exponential expression in Exercises 2364. 20b1"l0b20
 P.2.55: Simplify each exponential expression in Exercises 2364. (4x'f'
 P.2.56: Simplify each exponential expression in Exercises 2364. (10x'r'
 P.2.57: Simplify each exponential expression in Exercises 2364. 24xJ\ls 10...
 P.2.58: Simplify each exponential expression in Exercises 2364. 10x'y930xl...
 P.2.59: Simplify each exponential expression in Exercises 2364. e'
 P.2.60: Simplify each exponential expression in Exercises 2364. e;T
 P.2.61: Simplify each exponential expression in Exercises 2364. 15a"b2)' ...
 P.2.62: Simplify each exponential expression in Exercises 2364.  30a"b')'...
 P.2.63: Simplify each exponential expression in Exercises 2364. 3a b2 12 34
 P.2.64: Simplify each exponential expression in Exercises 2364. 4a b3 12ab5
 P.2.65: In Exerdses 6576. write each number in decimal notation without th...
 P.2.66: In Exerdses 6576. write each number in decimal notation without th...
 P.2.67: In Exerdses 6576. write each number in decimal notation without th...
 P.2.68: In Exerdses 6576. write each number in decimal notation without th...
 P.2.69: In Exerdses 6576. write each number in decimal notation without th...
 P.2.70: In Exerdses 6576. write each number in decimal notation without th...
 P.2.71: In Exerdses 6576. write each number in decimal notation without th...
 P.2.72: In Exerdses 6576. write each number in decimal notation without th...
 P.2.73: In Exerdses 6576. write each number in decimal notation without th...
 P.2.74: In Exerdses 6576. write each number in decimal notation without th...
 P.2.75: In Exerdses 6576. write each number in decimal notation without th...
 P.2.76: In Exerdses 6576. write each number in decimal notation without th...
 P.2.77: In Exercises 7786. write each number in scientific notation. 32,000
 P.2.78: In Exercises 7786. write each number in scientific notation. 64,000
 P.2.79: In Exercises 7786. write each number in scientific notation. 638,0...
 P.2.80: In Exercises 7786. write each number in scientific notation. 579,0...
 P.2.81: In Exercises 7786. write each number in scientific notation. 5716
 P.2.82: In Exercises 7786. write each number in scientific notation.  3829
 P.2.83: In Exercises 7786. write each number in scientific notation. 0.0027
 P.2.84: In Exercises 7786. write each number in scientific notation. 0.0083
 P.2.85: In Exercises 7786. write each number in scientific notation.  0.0...
 P.2.86: In Exercises 7786. write each number in scientific notation.  0.0...
 P.2.87: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.88: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.89: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.90: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.91: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.92: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.93: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.94: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.95: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.96: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.97: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.98: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.99: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.100: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.101: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.102: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.103: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.104: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.105: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.106: In Exercises 87106. perform the indicated computations. Write the ...
 P.2.107: In Exercises 107114. simplify each exponential expression. Assume ...
 P.2.108: In Exercises 107114. simplify each exponential expression. Assume ...
 P.2.109: In Exercises 107114. simplify each exponential expression. Assume ...
 P.2.110: In Exercises 107114. simplify each exponential expression. Assume ...
 P.2.111: In Exercises 107114. simplify each exponential expression. Assume ...
 P.2.112: In Exercises 107114. simplify each exponential expression. Assume ...
 P.2.113: In Exercises 107114. simplify each exponential expression. Assume ...
 P.2.114: In Exercises 107114. simplify each exponential expression. Assume ...
 P.2.115: The bar graph shows tire total amount Americans paid in federal tax...
 P.2.116: The bar graph shows tire total amount Americans paid in federal tax...
 P.2.117: In the dramatic. arts, ours is the era of the movies. As individual...
 P.2.118: In the dramatic. arts, ours is the era of the movies. As individual...
 P.2.119: The mass o f one oxygen molecule is 5.3 x 10n gram. Find the ma~f2...
 P.2.120: The mass of one hydrogen atom is 1.67 X 10 " gram. Find the mas~ o...
 P.2.121: There a re approximately 3.2 x 107 seconds in a year. According to ...
 P.2.122: Convert 365 days (one year) to hours, to minutes,and,finally, to se...
 P.2.123: Describe what it means to raise a number to a power. In your descri...
 P.2.124: Explain the product rule for exponents. Use 23 2s in your explanation.
 P.2.125: Explain the power rule for exponents. Use (32)"t in your explanation.
 P.2.126: Explain the quotient rule for exponents. Use 51 m your explanation.
 P.2.127: Why is ( 3x2)(2A') not simplified? What must be done to simplify ...
 P.2.128: How do you know if a number is written in scientific notation?
 P.2.129: Explain how to convert from scientific to decimal notation and give...
 P.2.130: Explain how to convert from decimal to scientific notation and give...
 P.2.131: Refer to Lhe Blitzer Bonus on page 32. Use scientific notation to v...
 P.2.132: In Exercises 132135, determine whether each statement makes sense ...
 P.2.133: In Exercises 132135, determine whether each statement makes sense ...
 P.2.134: In Exercises 132135, determine whether each statement makes sense ...
 P.2.135: In Exercises 132135, determine whether each statement makes sense ...
 P.2.136: In Exerdses 136143, determine k'hether e.acll statement is true or...
 P.2.137: In Exerdses 136143, determine k'hether e.acll statement is true or...
 P.2.138: In Exerdses 136143, determine k'hether e.acll statement is true or...
 P.2.139: In Exerdses 136143, determine k'hether e.acll statement is true or...
 P.2.140: In Exerdses 136143, determine k'hether e.acll statement is true or...
 P.2.141: In Exerdses 136143, determine k'hether e.acll statement is true or...
 P.2.142: In Exerdses 136143, determine k'hether e.acll statement is true or...
 P.2.143: In Exerdses 136143, determine k'hether e.acll statement is true or...
 P.2.144: The mad Dr. Frankenste in has gathered enough bits and pieces (so t...
 P.2.145: If 1Y'  MN,bc  M, and bD  N. what is the relationship among A, C...
 P.2.146: Our hearts beat approximately 70 times per minute. Express in scien...
 P.2.147: Putting l'iumbers into Perspective~ A large number can be put into ...
 P.2.148: Exercises 148150 wilf help you. prepare for the mateda/ covered in...
 P.2.149: Exercises 148150 wilf help you. prepare for the mateda/ covered in...
 P.2.150: Exercises 148150 wilf help you. prepare for the mateda/ covered in...
Solutions for Chapter P.2: Exponents and Scientific Notation
Full solutions for College Algebra  6th Edition
ISBN: 9780321782281
Solutions for Chapter P.2: Exponents and Scientific Notation
Get Full SolutionsChapter P.2: Exponents and Scientific Notation includes 150 full stepbystep solutions. Since 150 problems in chapter P.2: Exponents and Scientific Notation have been answered, more than 37104 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9780321782281. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 6.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

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.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Outer product uv T
= column times row = rank one matrix.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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.

Solvable system Ax = b.
The right side b is in the column space of A.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.