 5.6.1: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.2: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.3: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.4: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.5: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.6: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.7: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.8: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.9: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.10: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.11: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.12: In 112, use properties of exponents to simplify each expression. Fi...
 5.6.13: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.14: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.15: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.16: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.17: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.18: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.19: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.20: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.21: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.22: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.23: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.24: In 1324, use the zero and negative exponent rules to simplify each ...
 5.6.25: In 2530, use properties of exponents to simplify each expression. F...
 5.6.26: In 2530, use properties of exponents to simplify each expression. F...
 5.6.27: In 2530, use properties of exponents to simplify each expression. F...
 5.6.28: In 2530, use properties of exponents to simplify each expression. F...
 5.6.29: In 2530, use properties of exponents to simplify each expression. F...
 5.6.30: In 2530, use properties of exponents to simplify each expression. F...
 5.6.31: In 3142, use properties of exponents to simplify each expression. E...
 5.6.32: In 3142, use properties of exponents to simplify each expression. E...
 5.6.33: In 3142, use properties of exponents to simplify each expression. E...
 5.6.34: In 3142, use properties of exponents to simplify each expression. E...
 5.6.35: In 3142, use properties of exponents to simplify each expression. E...
 5.6.36: In 3142, use properties of exponents to simplify each expression. E...
 5.6.37: In 3142, use properties of exponents to simplify each expression. E...
 5.6.38: In 3142, use properties of exponents to simplify each expression. E...
 5.6.39: In 3142, use properties of exponents to simplify each expression. E...
 5.6.40: In 3142, use properties of exponents to simplify each expression. E...
 5.6.41: In 3142, use properties of exponents to simplify each expression. E...
 5.6.42: In 3142, use properties of exponents to simplify each expression. E...
 5.6.43: In 4358, express each number in decimal notation.2.7 * 10
 5.6.44: In 4358, express each number in decimal notation.4.7 * 103
 5.6.45: In 4358, express each number in decimal notation.9.12 * 105
 5.6.46: In 4358, express each number in decimal notation.4 * 104
 5.6.47: In 4358, express each number in decimal notation.8 * 107
 5.6.48: In 4358, express each number in decimal notation.7 * 106
 5.6.49: In 4358, express each number in decimal notation.. 1 * 105
 5.6.50: In 4358, express each number in decimal notation.. 1 * 108
 5.6.51: In 4358, express each number in decimal notation.7.9 * 101
 5.6.52: In 4358, express each number in decimal notation.8.6 * 101
 5.6.53: In 4358, express each number in decimal notation.2.15 * 102
 5.6.54: In 4358, express each number in decimal notation.3.14 * 102
 5.6.55: In 4358, express each number in decimal notation.7.86 * 104
 5.6.56: In 4358, express each number in decimal notation.4.63 * 105
 5.6.57: In 4358, express each number in decimal notation.3.18 * 106
 5.6.58: In 4358, express each number in decimal notation.5.84 * 107
 5.6.59: In 5978, express each number in scientific notation370
 5.6.60: In 5978, express each number in scientific notation530
 5.6.61: In 5978, express each number in scientific notation3600
 5.6.62: In 5978, express each number in scientific notation.2700
 5.6.63: In 5978, express each number in scientific notation.32,000
 5.6.64: In 5978, express each number in scientific notation.64,000
 5.6.65: In 5978, express each number in scientific notation.220,000,000
 5.6.66: In 5978, express each number in scientific notation.370,000,000,000
 5.6.67: In 5978, express each number in scientific notation.0.027
 5.6.68: In 5978, express each number in scientific notation.0.014
 5.6.69: In 5978, express each number in scientific notation.. 0.0037
 5.6.70: In 5978, express each number in scientific notation.0.00083
 5.6.71: In 5978, express each number in scientific notation.0.00000293
 5.6.72: In 5978, express each number in scientific notation.0.000000647
 5.6.73: In 5978, express each number in scientific notation.820 * 105
 5.6.74: In 5978, express each number in scientific notation.630 * 108
 5.6.75: In 5978, express each number in scientific notation.0.41 * 106
 5.6.76: In 5978, express each number in scientific notation.0.57 * 109
 5.6.77: In 5978, express each number in scientific notation.2100 * 109
 5.6.78: In 5978, express each number in scientific notation.97,000 * 1011
 5.6.79: In 7992, perform the indicated operation and express each answer in...
 5.6.80: In 7992, perform the indicated operation and express each answer in...
 5.6.81: In 7992, perform the indicated operation and express each answer in...
 5.6.82: In 7992, perform the indicated operation and express each answer in...
 5.6.83: In 7992, perform the indicated operation and express each answer in...
 5.6.84: In 7992, perform the indicated operation and express each answer in...
 5.6.85: In 7992, perform the indicated operation and express each answer in...
 5.6.86: In 7992, perform the indicated operation and express each answer in...
 5.6.87: In 7992, perform the indicated operation and express each answer in...
 5.6.88: In 7992, perform the indicated operation and express each answer in...
 5.6.89: In 7992, perform the indicated operation and express each answer in...
 5.6.90: In 7992, perform the indicated operation and express each answer in...
 5.6.91: In 7992, perform the indicated operation and express each answer in...
 5.6.92: In 7992, perform the indicated operation and express each answer in...
 5.6.93: In 93102, perform the indicated operation by first expressing each ...
 5.6.94: In 93102, perform the indicated operation by first expressing each ...
 5.6.95: In 93102, perform the indicated operation by first expressing each ...
 5.6.96: In 93102, perform the indicated operation by first expressing each ...
 5.6.97: In 93102, perform the indicated operation by first expressing each ...
 5.6.98: In 93102, perform the indicated operation by first expressing each ...
 5.6.99: In 93102, perform the indicated operation by first expressing each ...
 5.6.100: In 93102, perform the indicated operation by first expressing each ...
 5.6.101: In 93102, perform the indicated operation by first expressing each ...
 5.6.102: In 93102, perform the indicated operation by first expressing each ...
 5.6.103: In 103106, perform the indicated operations. Express each answer as...
 5.6.104: In 103106, perform the indicated operations. Express each answer as...
 5.6.105: In 103106, perform the indicated operations. Express each answer as...
 5.6.106: In 103106, perform the indicated operations. Express each answer as...
 5.6.107: In 107110, perform the indicated computations. Express answers in s...
 5.6.108: In 107110, perform the indicated computations. Express answers in s...
 5.6.109: In 107110, perform the indicated computations. Express answers in s...
 5.6.110: In 107110, perform the indicated computations. Express answers in s...
 5.6.111: The bar graph shows the total amount Americans paid in federal taxe...
 5.6.112: The bar graph shows the total amount Americans paid in federal taxe...
 5.6.113: The bar graph quantifies our love for movies by showing the number ...
 5.6.114: The bar graph quantifies our love for movies by showing the number ...
 5.6.115: The mass of one oxygen molecule is 5.3 * 1023 gram. Find the mass ...
 5.6.116: The mass of one hydrogen atom is 1.67 * 1024 gram. Find the mass o...
 5.6.117: There are approximately 3.2 * 107 seconds in a year. According to t...
 5.6.118: Convert 365 days (one year) to hours, to minutes, and, finally, to ...
 5.6.119: Explain the product rule for exponents. Use 23 # 25 in your explana...
 5.6.120: Explain the power rule for exponents. Use (32 ) 4 in your explanation.
 5.6.121: Explain the quotient rule for exponents. Use 58 52 in your explanat...
 5.6.122: Explain the zero exponent rule and give an example
 5.6.123: Explain the negative exponent rule and give an example.
 5.6.124: How do you know if a number is written in scientific notation?
 5.6.125: Explain how to convert from scientific to decimal notation and give...
 5.6.126: Explain how to convert from decimal to scientific notation and give...
 5.6.127: Suppose you are looking at a number in scientific notation. Describ...
 5.6.128: Describe one advantage of expressing a number in scientific notatio...
 5.6.129: Make Sense? In 129132, determine whether each statement makes sense...
 5.6.130: Make Sense? In 129132, determine whether each statement makes sense...
 5.6.131: Make Sense? In 129132, determine whether each statement makes sense...
 5.6.132: Make Sense? In 129132, determine whether each statement makes sense...
 5.6.133: In 133140, determine whether each statement is true or false. If th...
 5.6.134: In 133140, determine whether each statement is true or false. If th...
 5.6.135: In 133140, determine whether each statement is true or false. If th...
 5.6.136: In 133140, determine whether each statement is true or false. If th...
 5.6.137: In 133140, determine whether each statement is true or false. If th...
 5.6.138: In 133140, determine whether each statement is true or false. If th...
 5.6.139: In 133140, determine whether each statement is true or false. If th...
 5.6.140: In 133140, determine whether each statement is true or false. If th...
 5.6.141: Give an example of a number for which there is no advantage to usin...
 5.6.142: The mad Dr. Frankenstein has gathered enough bits and pieces (so to...
 5.6.143: Use a calculator in a fraction mode to check your answers in 1924.
 5.6.144: . Use a calculator to check any three of your answers in 4358.
 5.6.145: Use a calculator to check any three of your answers in 5978.
 5.6.146: Use a calculator with an EE or EXP key to check any four of your co...
 5.6.147: Putting Numbers into Perspective. A large number can be put into pe...
 5.6.148: Refer to the Blitzer Bonus on page 319. Group members should use sc...
Solutions for Chapter 5.6: Exponents and Scientific Notation
Full solutions for Thinking Mathematically  6th Edition
ISBN: 9780321867322
Solutions for Chapter 5.6: Exponents and Scientific Notation
Get Full SolutionsSince 148 problems in chapter 5.6: Exponents and Scientific Notation have been answered, more than 70461 students have viewed full stepbystep solutions from this chapter. Chapter 5.6: Exponents and Scientific Notation includes 148 full stepbystep solutions. This textbook survival guide was created for the textbook: Thinking Mathematically, edition: 6. Thinking Mathematically was written by and is associated to the ISBN: 9780321867322. 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.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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)·(b  Ax) = o.

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.