Section 8.1 Laws of Exponents: Multiplying monomials
Algebra I
Obj: define exponents and powers.
Obj: find products of powers.
Obj: simplify products of monomials.
Vocab
Base of a power  the # that is raised to an exponent. In an expression of the the form xa, x is the base.
Coefficient  a # that is multiplied by a variable.
Exponent in a power, the # that tells how many times the base is used as a factor. In an expression of
the form xa, a is the exponent.
Monomial  an algebraic expression that is either a constant, a variable, or a product of a constant and
one or more variables.
Product of powers property  if x is any # and m and n are intergers, then xm . xn = xm+n
xm  xn = xm+n
Simplify the product of monomials containing exponents.
Simplify (5c2d3)(7cd5)
Group terms with the same base.
= 35  c2  c  d3  d5
Use the Product-of-Powers Property.
= 35  c2 + 1  d3 + 5
Simplify
= 35c3d8
Section 8.2
Laws of Exponents: powers and products
Obj: Find the power of a power.
Obj: Find the power of a product.
Vocab
Power of a power property if x is any # and m and n are integers, then (xm)n
Power of a product property  if x and y are any # and n is an integer, then (xy)n = xnyn
Use the properties of exponents to simplify an expression.
Simplify n3(2k2n4)2
= n3  22  (k2)2(n4)2
Use the Power-of-a-Power Property.
= n3  4  k2(2)  n4(2)
= n3  4  k4  n8
Use the Product-of-Powers Property.
= 4  k4  n3+8
= 4k4n11
Powers of –1
Even powers of –1 are equal to 1.
Odd powers of –1 are equal to –1.
Algebra I
Section 8.3
Laws of Exponents: Dividing Monomials
Algebra I
Obj: simplify quotients of powers.
Obj: simplify powers of fractions.
Vocab
Power of a fraction property if n is an integer and a and b are #s, where b ≠ 0, then (a/b)n = an/bn
Quotient of powers property  if x is any # except 0 and ma and n are any positive integers, where m >
n then xm/xn = xm-n
Use the properties of exponents to simplify expressions containing fractions.
15x7y3
3xy2
Use the Quotient-of-Powers Property.
= 5x6y
Use the properties of exponents to simplify expressions containing fractions.
Use the Power-of-a-Fraction Property.
Section 8.4
Negative and Zero Exponents
Obj: Understand the concepts of negative and zero exponents.
Obj: Simplify expressions containing negative and zero exponents.
Vocab
Negative exponent  if x is any # except zero and n is a positive integer, then x-n = 1/xn
Zero as an exponent  for any nonzero # x, x0 = 1
Simplify expressions containing negative and zero exponents.
and write the expression with
positive exponents only.
= 7  x3 – 8  y2 – 1  z1 – 3
= 7x–5yz–2
Algebra I
Section 8.5
Scientific Notation
Algebra I
Obj: recognize the need for special notation in scientific calculations.
Obj: perform computations involving scientific notation.
Vocab
Scientific notation  a # written in scientific notation is a product of 2 factors: a # from 1 to 10,
including 1 but not including 10 and a power of 10.
Perform computations involving scientific notation.
Write (4  104)(7  105) in scientific notation.
= 28  109
= (2.8  101)(109)
= 2.8  1010
Section 8.6
Exponential Functions
Algebra I
Obj: understand exponential functions and how they are used.
Obj: recognize differences between graphs of exponential functions with different bases.
Vocab
Exponential function  a function of the form y = 2x in which a base # is raised to a variable exponent.
Exponential functions model situations in which values in the range change by a fixed rate rather than a
fixed amount.
General growth formula  Let A be the amount after t years at a yearly growth rate of r, where r is
expressed as a decimal. If the original amount is P, then the general growth formula is A=P(1+r)t
A = original amount
t = time in years
r = yearly growth rate expressed as a decimal
P = amount after t years
Understand and graph exponential functions.
The current population of a city is 275,000.
It is estimated that the population will grow at a rate of 2.2% per year.
What will the population be 6 years from now?
A = 275,000
P = A(1 + r)t
r = 0.022
P = 275,000(1.022)6
t=6
P  313,356
Section 8.7
Applications of Exponential Functions
Algebra I
Obj: use exponential functions to model applications that include growth and decay in different
contexts.
Vocab
Exponential decay a situation modeled by the general growth formula, A =P(1+r)t, in which r is
negative.
Exponential growth  a situation modeled by the general growth formula, A = P(1+r)t, in which r is
positive.
Use exponential functions to model applications.
The current population of a city is 403,000.
Over the last 10 years, the population has been decreasing at the rate of 1.6% per year.
What will the population be 6 years from now?
A = 403,000
P = A(1 + r)t
r = 1 – 0.016
P = 403,000(0.984)6
t=6
P  365,827