Apply Properties of Multiplying Integer Exponents

What if the chips represented 45 * 42?

What would be a simplified expression?

4 4 4 4 4 44 X X X X X*

Apply Properties of Multiplying Integer Exponents

Using your chips, create an equivalent expression for:

x4 * x2

Apply Properties of Multiplying Integer Exponents

What if the circles represented 45 * 4-2?

Apply Properties to Multiplying using Integer Exponents

What is the new expression?

Match positive and negative chips

How could you rewrite this expression?

Apply Properties to Multiplying using Integer Exponents

What is the new expression?

Apply Properties of Multiplying Integer Exponents

45 * 4-2 = 45 * 1/42

= 43 4 4

4 4 4 44 X X X X

X

Apply Properties of Multiplying Integer Exponents

Now use your chips for this problem:

x4 * x-2

Apply Properties to Dividing using Integer Exponents

What if the chips represented 46 / 42?

Simplify by reducing to 1

4 4 4 44 X X X X 4X

4 4X

Apply Properties to Dividing using Integer Exponents

Now you have

1 *

What is the simplified value?

Apply Properties to Dividing using Integer Exponents

What if the circles represented 46 / 4-3?

Simplify by reducing to 144 4

4 4 4 44 X X X X 4X

Apply Properties to Dividing using Integer Exponents

What does 1/4-3 mean?

43

Apply Properties to Dividing using Integer Exponents

So, 46 / 4-3 really means 46 * 43

Apply Properties to Dividing using Integer Exponents

What if the circles represented 46 / 46?

= 1

Simplify to reduce to 1

Apply Properties to Dividing using Integer Exponents

What if the circles represented 46 / 46?

Simplify to reduce to 1

Apply Properties to Dividing using Integer Exponents

Only thing left is…

1

So, a zero exponent means….

Properties of Integer Exponents• Positive exponents• Multiplication of integer

expressions• Negative exponents• Zero exponents• Division of integer expressions

Properties of Integer Exponents

• Positive exponents

• Ex: x4 = x * x * x *x

• 52 = 5 * 5 = 25

Properties of Integer Exponents• Multiplying Integer exponents• Equivalent to the base multiplied by itself

the amount of the exponent• x2 * x3 = x? =

2 + 3 = 5

What is a quick way to find the

exponent of theresult?

Properties of Integer Exponents• Negative exponents• Equivalent to the reciprocal of base

to the positive exponent• Ex: x-n = 1/xn

• 5-2 = (1/5)2 = 1/5 * 1/5 = 1/25

2

Properties of Integer Exponents

• Dividing Integer Exponents• Equivalent to the reciprocal of base

to the positive exponent• X4 / x2 = x?

4 + (-2) = -2

What is a quick way to find the

exponent of theresult?

Properties of Integer Exponents

• Zero exponents• Equivalent to the value 1

• Ex: x0 = 1• 50 = 1