Exponents!

Multiply 2 Groupings

100

(x^2)^2 * (y^2)

x^4 y^2

200

(x^2 y^3)^2 * (xy)

x^5 y^7

300

(x^2 y^3 z^4)^0 * (x^1 y^2 z^3 )^1

x y^2 z^3

400

(2x^3)^-1 * (2 x^2)^2

2x

500

(6a^4 b^-3 )^0 (-4ab^5 )

-4ab^5

What is equivalent?

100

(xyz)^0

1

200

(a^4)/b^6

a^4 b^-6

300

(a^5 * a^1)/(a^2 * a^3 * a^2)

a^-1

or

1/a

400

(-18c^8 d^9)/(9 c^3 d^9)

-2c^5

500

((2x y^4)/(14x^2 y^-3))^-2

(49x^2) / y^14

Variable Exponent

100

(g^4)^m = g^56

m = 14

200

(xyz)^m = 1

m = 0

300

(xyz)^m/(xyz)=xyz

m=2

400

x^m = 1/x^3

m=-3

500

(x^8)^m/(x^4)^-3 = x^28

m=2

Exponent Rules

100

What is the expanded form for 

(x)^2

x*x

200

Any value raised to the 1st power is equal to ______?

For example 

5^1 =

The original value

Example:  

5^1 = 5

300

Anything raised to the 0th power is?

1

400

What does a negative exponent do?

It means division, and it moves a term to either the top or bottom of a fraction bar depending on where it was before.  Example: 

x^-1 = 1/x

(1/x)^-1 = x/1

500

When do you add exponents?

When you are multiplying two terms of the same base

Examples: 

x^1 * x^1 = x^2

a^2 * a^5 = a^7

CHALLENGE

100

What is the value of 

2^4 =

16

200

What is the value of 

2^9

512

300

Why do we cross out a variable equal to one when multiplying?

For example:

2*x^0 = 2

1 times (or multiplied) by anything will be equal to the other value being multiplied.

Example:

67*1*1*1*1*1*1=67

400

When do we subtract exponents?

When dividing by two terms with the same variable base.

Example:

x^2 / x^1 = x^1

500

What is the Fundamental Theorem of Arithmetic?

Every positive integer can be represented by a UNIQUE prime factorization.

Example:

676767=3^1*7^1*13^1*37^1*67^1