 1.6.1: The product rule for exponents states that bm # bn = ______________...
 1.6.2: The quotient rule for exponents states that bm bn = ______________,...
 1.6.3: If b 0, then b0 = ______________.
 1.6.4: The negativeexponent rule states that bn = ______________, b 0.
 1.6.5: True or false: 52 = 52 ______________
 1.6.6: Negative exponents in denominators can be evaluated using 1 bn = _...
 1.6.7: True or false: 1 82 = 82 ______________
 1.6.8: 5x3 # 3x2
 1.6.9: (2y10 )(10y2 )
 1.6.10: (4y8 )(8y4 )
 1.6.11: (5x3y4 )(20x7y8 )
 1.6.12: (4x5 y6 )(20x7y4 )
 1.6.13: (3x4y0z)(7xyz3 )
 1.6.14: (9x3yz4 )(5xy0z2 )
 1.6.15: b12 b3
 1.6.16: b25 b5
 1.6.17: 15x9 3x4
 1.6.18: 18x11 3x4
 1.6.19: x9y7 x4y2
 1.6.20: x9y12 x2y6
 1.6.21: 50x2y7 5xy4
 1.6.22: 36x12y4 4xy2
 1.6.23: 56a12b10c 8 7ab2c 4
 1.6.24: 66a9b7c 6 6a3bc 2
 1.6.25: 60
 1.6.26: 90
 1.6.27: (4) 0
 1.6.28: (2) 0
 1.6.29: 40
 1.6.30: 20
 1.6.31: 13y0
 1.6.32: 17y0
 1.6.33: (13y) 0
 1.6.34: (17y) 0
 1.6.35: 32
 1.6.36: 42
 1.6.37: (5) 2
 1.6.38: (7) 2
 1.6.39: 52
 1.6.40: 72
 1.6.41: x2y3
 1.6.42: x3y4
 1.6.43: 8x7y3
 1.6.44: 9x8 y4
 1.6.45: 1 53
 1.6.46: 1 25
 1.6.47: 1 (3) 4
 1.6.48: 1 (2) 4
 1.6.49: x2 y5
 1.6.50: x3 y7
 1.6.51: a4b7 c3
 1.6.52: a3b8 c2
 1.6.53: (x6 ) 10
 1.6.54: (x3 ) 2
 1.6.55: (b4 ) 3
 1.6.56: (b8 ) 3
 1.6.57: (74 ) 5
 1.6.58: (94 ) 5
 1.6.59: (4x) 3
 1.6.60: (2x) 5
 1.6.61: (3x7 ) 2
 1.6.62: (4x9 ) 2
 1.6.63: (2xy2 ) 3
 1.6.64: (3x2y) 4
 1.6.65: (3x2y5 ) 2
 1.6.66: (3x4y6 ) 2
 1.6.67: (3x2 ) 3
 1.6.68: (2x4 ) 3
 1.6.69: (5x3y4 ) 2
 1.6.70: (7x2y5 ) 2
 1.6.71: (2x5y4z2 ) 4
 1.6.72: (2x4y5z3 ) 4
 1.6.73: a 2 x b 4
 1.6.74: a y 2 b 5
 1.6.75: x3 5 2
 1.6.76: x4 6 2
 1.6.77: a 3x y b 4
 1.6.78: a 2x y b 5
 1.6.79: x4 y2 6
 1.6.80: x5 y3 6
 1.6.81: x3 y4 3
 1.6.82: x4 y2 3
 1.6.83: a2 b3 4
 1.6.84: a3 b5 4
 1.6.85: x3 x9
 1.6.86: x6 x10
 1.6.87: 20x3 5x4
 1.6.88: 10x5 2x6
 1.6.89: 16x3 8x10
 1.6.90: 15x2 3x11
 1.6.91: 20a3b8 2ab13
 1.6.92: 72a5b11 9ab17
 1.6.93: x3 # x12
 1.6.94: x4 # x12
 1.6.95: (2a5 )(3a7 )
 1.6.96: (4a2 )(2a5 )
 1.6.97: a 1 4 x4y5 z1 b(12x3y1 z4 )
 1.6.98: a 1 3 x5y4 z6 b(18x2y1z7 )
 1.6.99: 6x2 2x8
 1.6.100: 12x5 3x10
 1.6.101: x7 x3
 1.6.102: x10 x4
 1.6.103: 30x2y5 6x8y3
 1.6.104: 24x2y13 2x5y2
 1.6.105: 24a3b5c 5 3a6b4c7
 1.6.106: 24a2b2c 8 8a5b1c3
 1.6.107: x3 x5 2
 1.6.108: x4 x11 3
 1.6.109: 15a4b2 5a10b3 3
 1.6.110: 30a14b8 10a17b2 3
 1.6.111: 3a5b2 12a3b4 0
 1.6.112: 4a5b3 12a3b5 0
 1.6.113: x5y8 3 4
 1.6.114: x6y7 2 3
 1.6.115: 20a3b4c 5 2a5b2c 2
 1.6.116: 2a4b3 c1 3a2b5c2 4
 1.6.117: 9y4 x2 + x1 y2 2
 1.6.118: 7x3 y9 + x1 y3 3
 1.6.119: 3x4 y4 1 2x y2 3
 1.6.120: 21x2y x4y1 2 xy3 x3y 3
 1.6.121: (4x3y5 ) 2 (2x8y5 )
 1.6.122: (4x4y5 ) 2 (2x5y6 )
 1.6.123: (2x2y4 ) 1 (4xy3 ) 3 (x2 y) 5 (x3y2 ) 4
 1.6.124: (3x3y2 ) 1 (2x2y) 2 (xy2 ) 5 (x2y3 ) 3
 1.6.125: a. What is the present aphid population? b. What will the aphid pop...
 1.6.126: a. What is the present aphid population? b. What will the aphid pop...
 1.6.127: a. How many people in the class started the rumor? b. How many peop...
 1.6.128: a. How many people in the class started the rumor? b. How many peop...
 1.6.129: Identify your answers to Exercise 127, parts (a) and (b), as points...
 1.6.130: Identify your answers to Exercise 128, parts (a) and (b), as points...
 1.6.131: Which one of the following best describes the rate of growth of the...
 1.6.132: Use the graph to determine how many people in the class eventually ...
 1.6.133: Substitute 1 for n and find the distance between Mercury and the sun.
 1.6.134: Substitute 2 for n and find the distance between Venus and the sun.
 1.6.135: How much farther from the sun is Jupiter than Earth?
 1.6.136: How much farther from the sun is Uranus than Earth?
 1.6.137: Explain the product rule for exponents. Use b2 # b3 in your explana...
 1.6.138: Explain the quotient rule for exponents. Use b8 b2 in your explanat...
 1.6.139: Explain how to find any nonzero number to the 0 power.
 1.6.140: Explain the negativeexponent rule and give an example.
 1.6.141: Explain the power rule for exponents. Use (b2 ) 3 in your explanation.
 1.6.142: Explain how to simplify an expression that involves a product raise...
 1.6.143: Explain how to simplify an expression that involves a quotient rais...
 1.6.144: How do you know if an exponential expression is simplified?
 1.6.145: Enter the rumor formula N = 25 1 + 24 # 2t in your graphing utilit...
 1.6.146: The properties (ab) n = anbn and a a b b n = an bn are like distrib...
 1.6.147: If 72 is raised to the third power, the result is a number between...
 1.6.148: There are many exponential expressions that are equal to 25x12 , su...
 1.6.149: The expression an b0 is undefined because division by 0 is undefined.
 1.6.150: 22 # 24 = 28
 1.6.151: 56 # 52 = 258
 1.6.152: 23 # 32 = 65
 1.6.153: 1 (2)3 = 23
 1.6.154: 28 23 = 25
 1.6.155: 24 + 25 = 29
 1.6.156: 2000.002 = (2 * 103 ) + (2 * 103 )
 1.6.157: 40,000.04 = (4 * 104 ) + (4 * 102 )
 1.6.158: xn1 # x3n+4
 1.6.159: (x4n # xn ) 3
 1.6.160: x3n x6n 2
 1.6.161: xny3n+1 yn 3
 1.6.162: Graph y = 2x  1 in a rectangular coordinate system. Let x = 3, 2...
 1.6.163: Solve Ax + By = C for y. (Section 1.5, Example 6)
 1.6.164: The length of a rectangular playing field is 5 meters less than twi...
 1.6.165: If 6.2 is multiplied by 103 , what does this multiplication do to t...
 1.6.166: If 8.5 is multiplied by 102 , what does this multiplication do to ...
 1.6.167: Write each computation as a single power of 10. Then evaluate this ...
Solutions for Chapter 1.6: Properties of Integral Exponents
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 1.6: Properties of Integral Exponents
Get Full SolutionsSince 167 problems in chapter 1.6: Properties of Integral Exponents have been answered, more than 29949 students have viewed full stepbystep solutions from this chapter. Chapter 1.6: Properties of Integral Exponents includes 167 full stepbystep solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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.

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

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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.

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

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

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

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).