Algebra: Chapter 5, Lesson 1, page 204.
Exponents!
Exponents and More with Exponents
Remember, an exponent tells how many times we use a base as a factor. For example, `a^3=a⋅a⋅a`. An expression written with exponents is written using exponential notation.
For like bases, we have:
- Rule: `a^0=1`
- Rule: to multiply we do `a^m⋅a^n=a^(m+n)
- Rule: to divide, we do `a^m/a^n=a^(m-n)`
- Rule: for negative exponent, we can express them as positive by, `a^(-m)=1/a^m
- Rule: for raising a power to another power, `(a^m)^n=a^(mn)`
- Rule: for raising a product to a power, `(ab)^n=a^n⋅b^n`
- Rule: for raising a quotient to a power, `(a/b)^n=a^n/b^n`
Remember and MEMORIZE THESE RULES for Lessons 1 and 2. Practice here!
They are also included in the Algebra Cheat Sheet that was passed today. As long as you remember these 7 formulae, you’ll be OK. Remember, if you forget the rules, just write out the problem and see what can be simplified!
PurpleMath has an EXCELLENT 2 page tutorial, click here!
Two of tonight’s homework problems solved by MrE are here! Just click it.
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Algebra 1a: Chapter 7, Lesson 4, page 318
Slope of a Line
The slope of a line is the tilt or slant. The slope is defined as the letter `m` and `m=(rise)/(run)`, where the `rise` is the change in the y-coordinate and the `run` is the change in the x-coordinate. This definition works great when you have 2 points on graph paper. You can just count the squares for the rise and the run. It doesn’t matter too, which point you start with.
Remember, slope is positive if the line is going from lower left to upper right. The slope is negative if its coming from upper left to lower right.
A slope of 0 is a horizontal line and a line with NO SLOPE is a vertical line.
Another definition of slope, given 2 point and NO GRAPH PAPER is:
`m=(y_2−y_1)/(x_2−x_1)`, where `(x_1,y_1)` and `(x_2,y_2)` are 2 points on the line.
For example, for the points (2, 3) and (-4, 2), the slope is:
`m = (2 – (-3))/(-4 – 2) = 5/(-6) = -(5/6)`
Purplemath has this link as well.
Two of tonight’s homework problems solved by MrE are here! Just click it.