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Thinking Mathematically

- Number Theory and the Real Number System
- 5.6 Exponents and Scientific Notation

Properties of Exponents

- The Product Rule Add exponents when multiplying

with the same base. Use the sum as the exponent

of the common base. bmbn bmn - The Power Rule Multiply exponents when an

exponential expression is raised to a power.

Place the product of the exponents on the base

and remove the parentheses. (bn)m bnm - The Quotient Rule Subtract exponents when

dividing with the same base. Use this difference

as the exponent of the common base. bm/bn bm -

n

Examples Properties of Exponents

- Exercise Set 5.6 3, 5, 11
- Use the properties of exponents to simplify, then

evaluate

The Zero Exponent Rule

- If b is any real number other than 0.
- b0 1
- Example
- 70 1
- p0 1
- (-5)0 1

The Negative Exponent Rule

- If b is any real number other than 0, and m is a

natural number, - Example
- 4-2 1/42 1/16
- 5-3 1/53 1/125
- 7-1 1/71 1/7

Exercise Set 5.6 19 2-2 ?

Properties of Exponents

- Example
- Exercise Set 5.6 27

Thinking Mathematically

- Number Theory and the Real Number System
- 5.6 Exponents and Scientific Notation

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