POD 22 AugEvaluate

•5x4; for x = 3

•(-3x)2; for x = 4

•(43 + 25) + 4

POD 29 Aug

• Solve for x1. 2x + 5 = 25

2. 30 + 5x = 50

3. 5x + 3x + 7 = 47

4. 25 = 2x + 5

For Printing

Mat h Zone

A =

L x

W

y = mx + b

3x+ 5 = 14

A = pr 2

Mat h Zone

A =

L x

W

y = mx + b

3x+ 5 = 14

A = pr 2

Exponents determine the number of times you use the

base as a factor.

32 = 3 x 3

54 = 5·5·5·5

11

What if the exponent is zero?What if the exponent is zero?

330334 = 81333 = 27332 = 9331 = 3330 =

Let’s Follow a PatternLet’s Follow a Pattern

=–1

–1

÷3

÷3

–1÷3

–1÷3

xx0=

Mat h Zone

A =

L x

W

y = mx + b

3x+ 5 = 14

A = pr 2

Mat h Zone

A =

L x

W

y = mx + b

3x+ 5 = 14

A = pr 2

?

Any number other than zero raised to the 0 power is always equal to 1 .

20 = 1,0000 =

100 = 300,0000 =

500 = x0 =

Any number raised to the first power is always equal to that number _itself_ .

11 = 21 = 181 = 141 = 1061 =

xx1= x

Parentheses• When a negative is enclosed in

parentheses the negative with the term

(-2)2 = (-2)(-2)

• When a negative is NOT enclosed in parentheses only the BASE is raised to a power

-22 = - 2·2

Parentheses

When a term is enclosed in parentheses the entire term is raised to the power

(2x)2 =

When a term is not enclosed in parentheses only the base is raised to a power

2x2 =

Parentheses

• When a term is enclosed in parentheses the ______________ is raised to the power

(2x)2 = 2x·2x• When a term is not enclosed in

parentheses _______________ is raised to a power

2x2 = 2·x·x

Lets try some with Numbers and Variables

X2 =

2X2 =

(2x)2 =

y3 = 4xy4 = 6x2y3 =

Lets try some with Numbers and Variables

X2 = x·x2X2 = 2·x·x(2x)2 = 2x·2x y3 = y·y·y4xy4 = 4·x·y·y·y·y6x2y3 = 6·x·x·y·y·y

For Printing

Mat h Zone

A =

L x

W

y = mx + b

3x+ 5 = 14

A = pr 2

Mat h Zone

A =

L x

W

y = mx + b

3x+ 5 = 14

A = pr 2

Now You Try:Z0= __________7,5631 = _________________4x5 = __________(3ab)3 = __________6ab2 = __________9a4b2c3 = ______________

Now You Try:Z0= __________7,5631 = _________________4x5 = __________(3ab)3 = __________6ab2 = __________9a4b2c3 = ______________

Quick Check

• Evaluate1. 52

2. (-5)2

3. -52

4. 50

5. 51

Expand6. (5x)2

7. 5x2

POD 30 Aug

Evaluate•-122

•(-12)2

•121

•120

Extension: Negative ExponentsExtension: Negative Exponents

332 = 9331 = 3330 = 1

Let’s Extend the PatternLet’s Extend the Pattern

–1 ÷3

–1 ÷3

–1 ÷3

33-1 = 1/3

33-2–1

÷3

= 1/9

=xx -1x1

xx –nxxn1=

=xx -1x1

xx –nxxn1=

Mat h Zone

A =

L x

W

y = mx + b

3x+ 5 = 14

A = pr 2

Mat h Zone

A =

L x

W

y = mx + b

3x+ 5 = 14

A = pr 2

To Evaluate Negative Exponents

• Take the Reciprocal of the base.• Change the negative exponent to a

positive exponent.• A negative exponent will always be a

value between 0 and 1. (Fraction or Decimal)

101 10 10-1 1 0.1

102 100 10-2 2 0.01

103 1000 10-3 3 0.001

100 = 1

1

10

10

1

1

100

10

1

10

1

1

1000

21 2 2 2-1

22 2x2 4 2-2

23 2x2x2 8 2-3

12

1

22

1

20 = 1

2

1

4

1