Scene 1

Scene 2

Scene 3

HERE IS A VIDEO TO START OUR LESSON.  ENJOY WATCHING!

Scene 4

Scene 5

Warm Up Evaluate each expression for the given values of the variables. 1.   x 3 y 2  for  x  = –1 and  y =  10 2.        for  x =  4 and  y =  (–7) Write each number as a power of the given base.

Scene 6

You have seen positive exponents. Recall that to simplify  3 2 , use  3  as a factor  2  times: 3 2  = 3    3 = 9.

But what does it mean for an exponent to be negative or 0? You can use a table and look for a pattern to figure it out.

Scene 7

When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5.

Scene 8

Base                        	      x                                     Exponent Remember!

Scene 9

Integer Exponents
WORDS
NUMBERS
3 = 1 1230=1
Zero exponent—Any
nonzero number raised to
the zero power is I.
Negative exponent—A
32
nonzero number raised to a
negative exponent is equal
to 1 divided by that number
24 ¯ 16
raised to the opposite
(positive) exponent.
ALGEBRA
If x + O, then xo— I.
If x + O and n is an integer,
then —
¯ xn•

Scene 10

Notice the phrase “nonzero number” in the previous table. This is because 0 0  and 0 raised to a negative power are both undefined. For example, if you use the pattern given above the table with a base of 0 instead of 5, you would get 0º =   . Also 0 –6  would be     =   . Since division by 0 is undefined, neither value exists.

Scene 11

2 –4  is read “2 to the negative fourth power.”  Reading Math

Scene 12

One cup is 2 –4  gallons. Simplify this expression.

Scene 13

A sand fly may have a wingspan up to 5 –3  m. Simplify this expression.

Scene 14

Any nonzero number raised to the zero power is 1.

Scene 15

In (–3) –4 , the base is negative because the negative sign is inside the parentheses. In –3 –4  the base (3) is positive.  Caution

Scene 16

Scene 17

Example 3A: Evaluating Expressions with Zero and Negative Exponents

Evaluate the expression for the given value of the variables.

Scene 18

Example 3B: Evaluating Expressions with Zero and Negative Exponents

Evaluate the expression for the given values of the variables.

–2 a 0 b -4  for  a  = 5 and  b =  –3

Write the power in the denominator as a product.

Scene 19

Evaluate the expression for the given value of the variable.

Scene 20

Scene 21

What if you have an expression with a negative exponent in a denominator, such as            ?

So if a base with a negative exponent is in a denominator, it is equivalent to the same base with the opposite (positive) exponent in the numerator.

An expression that contains negative or zero exponents is not considered to be simplified. Expressions should be rewritten with only positive exponents.

Scene 22

Example 4: Simplifying Expressions with Zero and Negative Numbers

Scene 23

Scene 24

Scene 25

1.  A square foot is 3 –2  square yards. Simplify this expression.  Simplify. 		 2.  2 –6 3.  (–7) –3   4.  6 0

Scene 26

Evaluate each expression for the given value(s) of the variables(s).

WELCOME TO GRADE 9 MATHEMATICS!

Page 1 (0s)

Page 2 (10s)

Page 3 (21s)

Page 4 (33s)

Page 5 (5m 33s)

Page 6 (6m 13s)

Page 7 (6m 53s)

Page 8 (7m 15s)

Page 9 (7m 27s)

Page 10 (7m 46s)

Page 11 (8m 8s)

Page 12 (8m 20s)

Page 13 (8m 34s)

Page 14 (8m 49s)

Page 15 (9m 8s)

Page 16 (9m 23s)

Page 17 (9m 39s)

Page 18 (9m 56s)

Page 19 (10m 29s)

Page 20 (10m 52s)

Page 21 (11m 24s)

Page 22 (11m 52s)

Page 23 (12m 15s)

Page 24 (12m 30s)

Page 25 (12m 56s)

Page 26 (13m 21s)