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BasicsBasics

What are exponents?• Exponents are shorthand for multiplication: • (5)(5) = 52 (5)(5)(5) = 53 • The "exponent" stands for however many

times the thing is being multiplied.• The thing that's being multiplied is called the

"base". • This process of using exponents is called

"raising to a power", where the exponent is the "power".

• "53" is "five, raised to the third power".

What are exponents?• When we deal with numbers, we

usually just simplify; we'd rather deal with "27" than with "33".

• But with variables, we need the exponents, because we'd rather deal with "x6" than with "xxxxxx".

Exponent Rules• There are a few rules that simplify

our dealings with exponents. Given the same base, there are ways that we can simplify various expressions. For instance:

…………………..

Rule 1: To multiply identical bases, add the exponents.

Example: 23 * 24 means: 2 * 2 * 2 * 2 * 2 * 2 * 2

If you count up all these 2’s it can be written as 27

According to Rule 1 though, we could have gotten the answer directly by adding the exponents (since they have the same base)

23 * 24 = 23+4 = 27

Practice w/ Rule 11. 53 * 510 =

2. Y8 * Y4 =

3. U7 * N5 =

Rule 2: To divide identical bases, subtract the

exponents.• Example: g6

g3 means g*g*g*g*g*g g*g*g

Which could be written as: g . g . g . g . g . g g g g or g3

Rule 2• According to rule 2 though, we

could have gotten the answer directly by subtracting (assuming the same base)

• g6

g3 is g 6-3 = g3

Practice w/ Rule 21. c90

c25

2. v14

v13

3. h4 * h3

h5

Rule 3: When there are two or more exponents and only one base, multiply the exponents.

Example: (t3)6 could be written as: t3 * t3 * t3 * t3 * t3 * t3

According to rule 1, we could all these exponents up (3+3+3+3+3+3) to arrive at our answer of t18.

But if we had used rule 3, we could have gone directly to the answer.

(t3)6 = t 3*6 = t18

Examples w/ Rule 31. (v10)5

2. (b8)6

3. (h5)3