Algebra 1: Chapter 1, Lesson 3, page 15.
Exponential Notation
A product in which the factors are the same is called a power. We can write `2⋅2⋅2⋅2` as `2^4`. The number 4 is called the exponent and the 2 is called the base. The exponent tells how many times the base is used as a factor. When an expression is written with exponents, we say the expression is written using exponential notation.
Remember, anything to the zero power is = 1, `z^0=1` or `4^0=1` as well. Anything raised to the 1 power is just the number, `y^1=y` and `101^1=101`.
Don’t forget PEMDAS too with the exponents being the second operation to be performed.
I like to use a site called purplemath.com. They have some great explanations about our lessons. See these explanations on exponents too!
Two of tonight’s homework problems solved by MrE are here! Just click it!!
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Algebra 1a: Chapter 1, Lesson 2, page 9.
The Commutative and Identity Properties
Commutative property is only for addition and multiplication.
`x+5=5+x`
`5*y=y*5`
Remember the identify properties of addition (0) and multiplication (1).
Anything to the 1st power is the number and anything to the 0 power is always = 1.
`z^1=z` and `z^0=1`
To form equivalent expressions, multiply the expression by `1/1` or variable/variable, like `y/y`. For example, convert `z/2` to an equivalent expression using `1/1` or `y/y`. To do this we have:
`z/2=z/2⋅y/y=zy/(2y)`
We can simplify algebraic expressions using the identity property for multiplication. For example, simplify `(xy)/(3y)`
`(xy)/(3y)=(x⋅y)/(3⋅y)=(x/3)⋅(y/y)=x/3`
Don’t forget, please put your first and last name on homework pages and make sure that I can read it. Show all work as well!!
Here is a link to tonight’s homework on Chapter 1, Lesson 2. There are 2 solutions provided. Remember, you need to have Quicktime for either the PC or Mac installed on your computer!