 7.2.1: In Exercises 120, use radical notation to rewrite each expression. ...
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 7.2.21: In Exercises 2138, rewrite each expression with rational exponents.27
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 7.2.39: In Exercises 3954, rewrite each expression with a positive rational...
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 7.2.55: In Exercises 5578, use properties of rational exponents to simplify...
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 7.2.79: In Exercises 79112, use rational exponents to simplify each express...
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 7.2.113: In Exercises 113116, use the distributive property or the FOIL meth...
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 7.2.117: In Exercises 117120, factor out the greatest common factor from eac...
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 7.2.125: models the number of plant species, f(x), on the various islands of...
 7.2.126: models the number of plant species, f(x), on the various islands of...
 7.2.127: The function f(x) = 70x 3 4 models the number of calories per day, ...
 7.2.128: The function f(x) = 70x 3 4 models the number of calories per day, ...
 7.2.129: The windchill temperatures shown in the table can be calculated usi...
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 7.2.133: Your job is to determine whether or not yachts are eligible for the...
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 7.2.139: In simplifying 36 3 2, is it better to use a m n = 2 n am or a m n ...
 7.2.140: How can you tell if an expression with rational exponents is simpli...
 7.2.141: Explain how to simplify 3 1x # 1x.
 7.2.142: Explain how to simplify 3 21x.
 7.2.143: Use a scientific or graphing calculator to verify your results in E...
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 7.2.145: Exercises 145147 show a number of simplifications, not all of which...
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 7.2.148: Make Sense? In Exercises 148151, determine whether each statement m...
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 7.2.156: A mathematics professor recently purchased a birthday cake for her ...
 7.2.157: The birthday boy in Exercise 156, excited by the inscription on the...
 7.2.158: Simplify: 33 + 127 2 3 + 32 2 5 2 4 3 2  9 1 2.
 7.2.159: Find the domain of f(x) = (x  3) 1 2(x + 4)  1 2.
 7.2.160: Write the equation of the linear function whose graph passes throug...
 7.2.161: Graph y  3 2 x + 3. (Section 4.4, Example 2)
 7.2.162: Solve by Cramers rule: e 5x  3y = 3 7x + y = 25. (Section 3.5, Exa...
 7.2.163: Exercises 163165 will help you prepare for the material covered in ...
 7.2.164: a. Find 216 # 24. b. Find 216 # 4. c. Based on your answers to part...
 7.2.165: a. Use a calculator to approximate 2300 to two decimal places. b. U...
 7.2.166: Simplify: a. 3 2x21 b. 6 2y24 .
Solutions for Chapter 7.2: Rational Exponents
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 7.2: Rational Exponents
Get Full SolutionsIntermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Chapter 7.2: Rational Exponents includes 166 full stepbystep solutions. Since 166 problems in chapter 7.2: Rational Exponents have been answered, more than 36996 students have viewed full stepbystep solutions from this chapter.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Column space C (A) =
space of all combinations of the columns of A.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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