TO MULTIPLY POWERS HAVING THE SAME BASE OBJECTIVE TO MULTIPLY POWERS HAVING THE SAME BASE

Pick up Homework and Quiz Test Chapter 3 25min max Start Chapter 5 Math 083 Bianco 2/22/10 Pick up Homework and Quiz Test Chapter 3 25min max Start Chapter 5

Today we will... use multiplication properties of exponents to evaluate and simplify expressions.

BASE EXPONENT EXPONENTIAL FORM FACTORED FORM COEFFICIENT VOCABULARY BASE EXPONENT EXPONENTIAL FORM FACTORED FORM COEFFICIENT

Exponents What is an exponent? What does xn mean? x is called the base. n is called the exponent. x is raised to the nth power.

{ Exponents xn = x • x • x ....... x n factors of x x = base n = exponent xn = x to the nth power

Find numerical answers: 1)26 2) 38 3) 44 4) (22)3 5) (34)2 6) (42)2 ??????????????????? Find numerical answers: 1)26 2) 38 3) 44 4) (22)3 5) (34)2 6) (42)2

Find numerical answers: 1)26 2) 38 3) 44 64 6561 256 ??????????????????? Find numerical answers: 1)26 2) 38 3) 44 64 6561 256 4) (22)3 5) (34)2 6) (42)2

Exponents x3 • x2 =

Exponents x3 • x2 = x • x • x • x • x { {

Exponents x3 • x2 = x • x • x • x • x { { 3 factors of x

{ { Exponents x3 • x2 = x • x • x • x • x 3 factors of x 2 factors

{ { Exponents x3 • x2 = x • x • x • x • x = x5 3 factors of x

Rules for Exponents Let a be any number and m and n be integers. 1. am • an =

Rules for Exponents Let a be any number and m and n be integers. 1. am • an = am + n

Rules for Exponents Let a be any number and m and n be integers 1. am • an = am + n Write the rule in words:

The Product Rule Product Rule for Exponents If m and n are positive integers and a is a real number, then am · an = am+n Example: Use the product rule to simplify. 32 · 34 = 32+4 = 36 = 3 · 3 · 3 · 3 · 3 · 3 = 729 z3 · z2 · z5 = z3+2+5 = z10 (3y2)(– 4y4) = 3 · y2 (– 4) · y4 = 3(– 4)(y2 · y4) = – 12y6

Product of Powers Rules for Exponents To multiply powers with like bases add the exponents, keep the base the same. Product of Powers

Simplify 1. c8 • c10 = c (10+8) = c 18

Simplify 2. b4 • b7 • b5 = b (4 +7 + 5) = b16

Keep base the same and add exponents an am = am+n Product of powers Keep base the same and add exponents an am = am+n ex: ( 3x2) (–5x4) = (3)(–5)(x2 ) (x4 ) = -15 x6

Simplify: 3) (x35)(x23) 4) (43)(42) 5) (–x5)(–x7)(x3)(x2) 6) (–1)25

Simplify: 3) (x35)(x23) = x58 4) (43)(42)= 45 5) (–x5)(–x7)(x3)(x2) = x17 6) (–1)25 = – 1

b 3 b 7 = b 2 b 3 = c 6 c 5 = x 5 x = m 4 m = (x) (x) (x) = Complete # 1- 7 m 3 m 2 = b 3 b 7 = b 2 b 3 = c 6 c 5 = x 5 x = m 4 m = (x) (x) (x) =

( c2 )3 = ( c2 ) ( c2 ) ( c2 )= c6

( x 8)3 = ( x 8) ( x 8) ( x 8) = x24

Zero Exponent Zero Exponent If a does not equal 0, then a0 = 1. Example: Simplify each of the following expressions. 50 = 1 (xyz3)0 = x0 · y0 · (z3)0 = 1 · 1 · 1 = 1 –x0 = –(x0) = – 1

The Quotient Rule Quotient Rule for Exponents If a is a nonzero real number and m and n are integers, then Example: Simplify the following expression. Group common bases together

Negative Exponents Negative Exponents If a is a real number other than 0 and n is a positive integer, then Example: Simplify by writing each of the following expressions with positive exponents or calculating. Remember that without parentheses, x is the base for the exponent –4, not 2x

Assignment # 2 5.1 #’s 1, 5, 9, 13, 17, 19, 25, 27, 31, 43, 45, 47, 53, 55, 65, 69, 77, 81, 83 5.2 #’s 3- 33 multiples of 3 i.e. 3, 6, 9 , …

BASE EXPONENT EXPONENTIAL FORM FACTORED FORM COEFFICIENT VOCABULARY BASE EXPONENT EXPONENTIAL FORM FACTORED FORM COEFFICIENT

Exponents What is an exponent? What does xn mean? x is called the _____. n is called the _____. x is raised to the nth ____.

Assignment # 2 5.1 #’s 1, 5, 9, 13, 17, 19, 25, 27, 31, 43, 45, 47, 53, 55, 65, 69, 77, 81, 83 5.2 #’s 3- 33 multiples of 3 i.e. 3, 6, 9 , …

Exponents { xn = x • x • x ....... x n factors of x x = n = xn =

Find numerical answers: 1)26 2) 38 3) 44 4) (22)3 5) (34)2 6) (42)2 ??????????????????? Find numerical answers: 1)26 2) 38 3) 44 4) (22)3 5) (34)2 6) (42)2

Exponents x3 • x2 =

Simplify 1. c8 • c10 =

Simplify 2. b4 • b7 • b5

Simplify: 3) (x35)(x23) 4) (43)(42) 5) (–x5)(–x7)(x3)(x2) 6) (–1)25

Keep base the same and add exponents an am = am+n ex: ( 3x2) ( -5x4) = Product of powers Keep base the same and add exponents an am = am+n ex: ( 3x2) ( -5x4) =

Multiply the following 1. a4 ( a3) ( a) 2. ( 3x3 ) ( -2x4 )

Evaluate if x = 3 and y = -5 x3 + y4 2. Divide (3x5y2 )/ (9x2y5) 3. Mult 3x3 (-2 x5 )