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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


This is the same answer we would get if we
added the exponents:

•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



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



•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 ×10r  , where 1 ≤ n ≤ 10 and r = an integer

•EX: write 454,000 in scientific notation.  4.54 ×105 

•Ex: what number is  3.28 ×104  ? 32,800

→Mixed Classwork: (or hand out worksheet?)

Break into groups and complete the following: