Download Unit 2 * quadratic, polynomial, and radical equations and inequalities

UNIT 2 –
QUADRATIC,
POLYNOMIAL, AND
RADICAL
EQUATIONS AND
INEQUALITIES
Chapter 6 – Polynomial
Functions
6.1 – Properties of Exponents
6.1 – PROPERTIES OF EXPONENTS
 In this section we will review:
 Using properties of exponents to multiply and divide monomials
 Using expressions written in scientific notation
6.1 – PROPERTIES OF EXPONENTS
 To simplify an expression containing powers means to rewrite the
expression without parentheses or negative exponents
 Negative exponents are a way of expressing the multiplicative inverse of a number
 1/x2 = x
-2
6.1 – PROPERTIES OF EXPONENTS
Negative Exponents
For any real number a ≠ 0 and any integer n, a
1 / an
2
-3
= 1 / 23 = 1 / 8
1/b
-8
=b8
–n
=
6.1 – PROPERTIES OF EXPONENTS
 Example 1
 Simplify each expression
 (-2 a3b)(-5 ab4)
 (3a5)(c -2)(-2a -4b3)
6.1 – PROPERTIES OF EXPONENTS
 Product of Powers
 For any real number a and integers m and n, am · an =
am + n
 42 · 49 = 411
 b3 · b5 = b8
 To multiply powers of the same variable, add the
exponents.
6.1 – PROPERTIES OF EXPONENTS
Quotient of Powers
For any real number a ≠ 0, and any integers m and
n, am/ an = am – n
 53 / 5 = 53
– 1
= 52 and x7/x3 = x7 – 3 = x4
To divide powers of the same base, you subtract
exponents
6.1 – PROPERTIES OF EXPONENTS
 Example 2
 Simplify s2 / s10 . Assume that s ≠ 0.
6.1 – PROPERTIES OF EXPONENTS
 Properties of Powers
 Suppose a and b are real numbers and m and n are integers. Then the
following properties hold.
 Power of a Power: (am)n = amn
 (a2)3 = a6
 Power of a Product: (ab)m = amam
 (xy)2 = x2y2
 Power of a Quotient: (a / b)n = an / an, b ≠ 0
 (a / b)3 = a3 / b3
 Power of a Quotient: (a / b)-n = (b / a)n or bn / an, a ≠0, b ≠0
 (x / y)-4 = y4 / x4
 Zero Power: a0 = 1, a ≠ 0
6.1 – PROPERTIES OF EXPONENTS
 Example 3
 Simplify each expression
 (-3c2d5)3
 (-2a / b2)5
6.1 – PROPERTIES OF EXPONENTS
 Example 4
 Simplify (-3a5y / a6yb4)5
6.1 – PROPERTIES OF EXPONENTS
 Standard notation – form in which numbers are usually written
 Scientific Notation – a number in form a x 10n, where 1 ≤ a < 10 and
n is an integer.
 Real world problems using numbers in scientific notation often involve units of
measure.
 Performing operations with units is know as dimensional analysis
6.1 – PROPERTIES OF EXPONENTS
 Example 5
 There are about 5 x 106 red blood cells in one milliliter of blood. A certain blood
sample contains 8.32 x 106 red blood cells. About how many milliliters of blood are
in the sample?
6.1 – PROPERTIES OF EXPONENTS
HOMEWORK
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