Watch “Powers of 10”

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Evaluating Exponents with Negative Bases

1. (–4)2

(–4)•(–4)

16

Since the negative sign is inside the parenthesis, keep it with the “4” when you multiply.

Since the negative sign is outside the parenthesis, leave it alone until the end.

Multiply 4•4...

Then, add the negative sign.3) –(3)3 4) (–3)3 5) –(2)5 6) (–2)5 7) –(1)7 8) (–7)1 –(3)•(3)•(3) (–3)•(–3)•(–3) –(2)•(2)•(2)•(2)•(2) (–2)•(–2)•(–2)•(–2)•(–2) –

(1)•(1)•(1)•(1)•(1)•(1)•(1) (–7)–(27) or –27 –27 –(32) or –32 –32 –(1) or –1 –7

2. – (4)2

–(4)•(4)

–( 16 )

–16ODD EXPONENTS

EVEN EXPONENTS

9) –(3)2 10) (–3)2 11) –(2)4 12) (–2)4 13) –(1)6 14) (–7)2

–(3)•(3) (–3)•(–3) –(2)•(2)•(2)•(2) (–2)•(–2)•(–2)•(–2) –(1)•(1)•(1)•(1)•(1)•(1) (–

7)•(–7) –(9)or –9 9 –(16) or –16 16 –(1) or –1

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Evaluating Exponents to the Zero Power, x0

1. 40 Everything to the zero power is 1.

40 = 1

2. (–4)0 Since the negative sign is inside the parenthesis (–), take the whole thing, –4, to the zero power.

Everything, even negative integers, to the zero power is 1.

(–4)0 = 1

3. –(4)0

–(40)–(1)

4. –(3.6)0 5. (–7)0 6. 610 7 . –20 8. (–10)0

–(3.6)0 = –1

(–7)0 = 1 610 = 1 –(2)0 = –1 (–10)0 = 1

Since the negative sign is outside the parenthesis, leave the negative sign alone.

Only take 4 to the zero power.

At the end, add the negative sign.–1

A plant grows when its cells divide into pairs, as shown below. What is another way to write the number of cells after the fourth division?

After the fourth cell division described above, there are 2 • 2 • 2 • 2 cells.= 24 There are 24

cells after the fourth cell division.

Understanding Exponents

2 • 2 • 2 • 2

The “2” is called the base.

The power of “4” is called the exponent.

Evaluating Exponents

Understanding Exponents

Evaluating Exponents

Writing Negative Exponents as Fractions

1. 6–3To evaluate a negative exponent, look at this pattern.

63

= 6•6•6 = 216

62

= 6•6 = 36

61

= 6 = 6What’s another way to get from 216 --> 36 ?Divide by

6.So, if you decrease the exponent by 1, divide by 6.

60

= 6 ÷ 6 = 1

6–1

= 1 ÷ 6 =

6–2

= ÷ =

6–3

= ÷ 6 =

÷ 6

61

61

361

Do you notice a shortcut for finding

the value of negative exponents?

If 62

= 36 .. and

6-2 = 1 .

36 ... then, what’s the value of...

361

216

116

Remember:

1. KEEP2. CHANGE 3. FLIP

If 63 = 216, ..

Evaluate each exponent term

Writing Negative Exponents as Fractions

Writing Negative Exponents as Decimals

there it is