 1.2.1: Is 23 the same as 32 ? Explain.
 1.2.2: When can you add two exponents?
 1.2.3: What is the purpose of scientific notation?
 1.2.4: Explain what a negative exponent does.
 1.2.5: For the following exercises, simplify the given expression. Write a...
 1.2.6: For the following exercises, simplify the given expression. Write a...
 1.2.7: For the following exercises, simplify the given expression. Write a...
 1.2.8: For the following exercises, simplify the given expression. Write a...
 1.2.9: For the following exercises, simplify the given expression. Write a...
 1.2.10: For the following exercises, simplify the given expression. Write a...
 1.2.11: For the following exercises, simplify the given expression. Write a...
 1.2.12: For the following exercises, simplify the given expression. Write a...
 1.2.13: For the following exercises, simplify the given expression. Write a...
 1.2.14: For the following exercises, simplify the given expression. Write a...
 1.2.15: For the following exercises, write each expression with a single ba...
 1.2.16: For the following exercises, write each expression with a single ba...
 1.2.17: For the following exercises, write each expression with a single ba...
 1.2.18: For the following exercises, write each expression with a single ba...
 1.2.19: For the following exercises, write each expression with a single ba...
 1.2.20: For the following exercises, write each expression with a single ba...
 1.2.21: For the following exercises, express the decimal in scientific nota...
 1.2.22: For the following exercises, express the decimal in scientific nota...
 1.2.23: For the following exercises, convert each number in scientific nota...
 1.2.24: For the following exercises, convert each number in scientific nota...
 1.2.25: For the following exercises, simplify the given expression. Write a...
 1.2.26: For the following exercises, simplify the given expression. Write a...
 1.2.27: For the following exercises, simplify the given expression. Write a...
 1.2.28: For the following exercises, simplify the given expression. Write a...
 1.2.29: For the following exercises, simplify the given expression. Write a...
 1.2.30: For the following exercises, simplify the given expression. Write a...
 1.2.31: For the following exercises, simplify the given expression. Write a...
 1.2.32: For the following exercises, simplify the given expression. Write a...
 1.2.33: For the following exercises, simplify the given expression. Write a...
 1.2.34: For the following exercises, simplify the given expression. Write a...
 1.2.35: For the following exercises, simplify the given expression. Write a...
 1.2.36: For the following exercises, simplify the given expression. Write a...
 1.2.37: For the following exercises, simplify the given expression. Write a...
 1.2.38: For the following exercises, simplify the given expression. Write a...
 1.2.39: For the following exercises, simplify the given expression. Write a...
 1.2.40: For the following exercises, simplify the given expression. Write a...
 1.2.41: For the following exercises, simplify the given expression. Write a...
 1.2.42: For the following exercises, simplify the given expression. Write a...
 1.2.43: For the following exercises, simplify the given expression. Write a...
 1.2.44: To reach escape velocity, a rocket must travel at the rate of 2.2 1...
 1.2.45: A dime is the thinnest coin in U.S. currency. A dimes thickness mea...
 1.2.46: The average distance between Earth and the Sun is 92,960,000 mi. Re...
 1.2.47: A terabyte is made of approximately 1,099,500,000,000 bytes. Rewrit...
 1.2.48: The Gross Domestic Product (GDP) for the United States in the first...
 1.2.49: One picometer is approximately 3.397 1011 in. Rewrite this length u...
 1.2.50: The value of the services sector of the U.S. economy in the first q...
 1.2.51: For the following exercises, use a graphing calculator to simplify....
 1.2.52: For the following exercises, use a graphing calculator to simplify....
 1.2.53: For the following exercises, simplify the given expression. Write a...
 1.2.54: For the following exercises, simplify the given expression. Write a...
 1.2.55: For the following exercises, simplify the given expression. Write a...
 1.2.56: For the following exercises, simplify the given expression. Write a...
 1.2.57: For the following exercises, simplify the given expression. Write a...
 1.2.58: Avogadros constant is used to calculate the number of particles in ...
 1.2.59: Plancks constant is an important unit of measure in quantum physics...
Solutions for Chapter 1.2: EXPONENTS AND SCIENTIFIC NOTATION
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 1.2: EXPONENTS AND SCIENTIFIC NOTATION
Get Full SolutionsSince 59 problems in chapter 1.2: EXPONENTS AND SCIENTIFIC NOTATION have been answered, more than 34048 students have viewed full stepbystep solutions from this chapter. Chapter 1.2: EXPONENTS AND SCIENTIFIC NOTATION includes 59 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781938168383.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

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.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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

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

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

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.