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# Section 12.1: Exponents

**Review Terms, monomials, degree**

Core Concepts:

**Review: exponents, bases, and negative and positive numbers raised to a
power; also review the
terms squared and cubed.**

Core Concepts:

→Product Rule: Multiplying two expressions with same base: Add exponents and use the

•common base

•

•EX:

This is the same answer we would get if we |

•So if we have two variables:

•What if we have ?

• Remember 2x is the same as2 times x or 2(x) .

• So, we can multiply the last two terms together using property 1 like so:

• Don’t try to include the number “2” in adding the
exponents because it is not the same

base as the variable “x” and is not included in the exponent “3” (as it would be
if it

were in parenthesis, i.e.(2x)^{3} - I’ll show you this in a minute.

→Power Rule: A power **raised to another power** is the base raised to the
product of the

powers

•

•EX:

•So

→Power of Product Rule: The power of a product is the product of a power

•

•EX:

•So

•And we can put several rules together:

→**NOTE**: The above properties only work when we are
dealing with **multiplication** of the

bases – they DO NOT work with addition of the bases

•**EX**: because
exponents are a form of multiplication. The only operation

we have is multiplication, so we are just using the commutative property to do
the

multiplication in a different order.

•**BUT you cannot do this with addition:** (a + b)^{r} because this
is a mix of addition and

multiplication and groups. **We must do the group FIRST!
**

•Try this with (2 + 3)

^{2}

by first following the order of operations, then trying to use the

property above. You’ll see that the second answer is incorrect, because we broke the

LAW – order of operations.

•Class work determine which property to use, then simplify:

→Scientific Notation

•Definition: a number written as the product of a number between 1 and 10 and an
integer

power of 10. A number written in scientific notation has the form:

•

n ×10^{r} , where 1 ≤ n ≤ 10 and r = an integer

•EX: write 454,000 in scientific notation. 4.54 ×10^{5}

•Ex: what number is 3.28 ×10^{4} ? 32,800

**→Mixed Classwork: (or hand out worksheet?)**

Break into groups and complete the following: