 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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 7.2.113: 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, ...
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 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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 7.2.141: 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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 7.2.156: 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 29683 students have viewed full stepbystep solutions from this chapter.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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.)

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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

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.

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].

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

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

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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·

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

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