 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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 7.2.27: In Exercises 2138, rewrite each expression with rational exponents.2x3
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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...
 7.2.130: 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...
 7.2.134: Your job is to determine whether or not yachts are eligible for the...
 7.2.135: What is the meaning of a 1 n? Give an example to support your expla...
 7.2.136: What is the meaning of a m n ? Give an example
 7.2.137: What is the meaning of a m n ? Give an example
 7.2.138: Explain why a 1 n is negative when n is odd and a is negative. What...
 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...
 7.2.144: Use a scientific or graphing calculator to verify your results in E...
 7.2.145: Exercises 145147 show a number of simplifications, not all of which...
 7.2.146: Exercises 145147 show a number of simplifications, not all of which...
 7.2.147: Exercises 145147 show a number of simplifications, not all of which...
 7.2.148: Make Sense? In Exercises 148151, determine whether each statement m...
 7.2.149: Make Sense? In Exercises 148151, determine whether each statement m...
 7.2.150: Make Sense? In Exercises 148151, determine whether each statement m...
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 7.2.152: In Exercises 152155, determine whether each statement is true or fa...
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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 16475 students have viewed full stepbystep solutions from this chapter.

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

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.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

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

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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 .

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

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

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

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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

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.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

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