Essential Question: What is the first step for simplifying an exponential expression that contains negative exponents?
1) Zero as an exponent Any number to the 0 power equals 1 Why?▪ x3 = 1x • 1x • 1x▪ x7 = 1x • 1x • 1x • 1x • 1x • 1x • 1x▪ x0 = no “x”s, so we leave just a “1”
2) Negative exponents Any number to a negative exponent moves
the base to the opposite side of a fraction, and the exponent becomes positive
Simplify: 4-3
Negative exponent. Move the base.
34
1341
Make the exponent positive.
1
64
Simplifying Expressions Simplify 4y0x-3
4 0y 3x
Exponent of 0 = 1
1
Move negative exponentMake exponent positive
3x 3
4
x
YOUR TURN – Simplify each expression 3-4
-70
11m-5
0 5
1 2
7
2
s t
m
1
2 5 2 5
7 2 1 14
m t m t
5
11
m
4
1 1
3 81
1
Multiplying Same Bases (add) When two numbers are multiplied
together and have the same base, their exponents are added.
Why?▪ x3 = x • x • x▪ x5 = x • x • x • x • x▪ x3 • x5 = x • x • x • x • x • x • x • x = x8
▪ x3 • x5 = x3+5 = x8
Dividing Same Bases (subtract) When two numbers are divided and have the
same base, their exponents are subtracted. Why?▪ x3 = x • x • x▪ x5 = x • x • x • x • x▪
2
5 2
5
35 2
3
3
1 1
1
x x x x x
x x x x
x x x
x xx
x
x
x
Power to a power (multiply) If an exponent is raised to a power
(typically outside a parenthesis), multiply the exponents together.
Examples:▪ (3x2y3)4 = 34x8y12
= 81x8y12
▪ 31 3 3 6
2 6 3
2 ( 2) 8x x y
y y x
YOUR TURN – Simplify each expression (7a2)(-2a-5)
5 2
3 2
2ab c
a bc
42 4 0
2
22
ba b c
a
33
1414a
a
Assignment Page 368 1 – 24 (all)
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