2.
Reminder of what an exponent is.<br />Base<br />
3.
A bunch of rules!<br />In the textbook’s P.2, there are a bunch of rules listed. (Some are on or near page 12.)<br />To save class time, I will present these rules simultaneous with example problems so you see them in practice, which is the most important part. <br />If you want the list of rules to copy in your notes, see the book. <br />
4.
Simplify (-3ab4)(4ab-3)<br />So the actions we took here could be said:<br />______________________________________<br />
5.
What was the exponent rule used?<br />When you multiply things with the SAME BASE, you add the exponents.<br />For example, a∙a = a1∙a1 = a2<br />Also, b4∙b-3 = b1 = b<br />
6.
(2xy2)3uses a different rule:<br />1st step is like “distributing” the exponent.<br /> = (2)3 (x)3 (y2)3 draw little arrows<br />2nd step uses a rule that when you take a power of a power, you multiply the exponents. [so (y2)3 would become y6]<br /> = 8x3y6 is the final answer.<br />
7.
3a(-4a2)0 uses another rule.<br />A rule says that ANYTHING to the zero power is ONE. <br /> = 3a∙1<br /> = 3a<br />Be careful not to jump to conclusions and automatically put down ONE as the answer to the entire problem: common mistake made.<br />
8.
uses a different rule<br />(kind of like “distributing” the exponent to the top and the bottom)<br />
9.
uses a different rule<br />If you are dividing and they have the same base, subtract the exponents. Seem reasonable?<br />
10.
rule giving meaning to negative exponents<br />If you ever have a negative exponent in your answer, you will need to change it to a positive by crossing it over the magic division bar.<br />Change to<br />Change to<br />
11.
Changing these to positive exponents<br />x -1 =<br />
14.
Rules that give meaning to sqrts<br />Square root of thirty six:<br />Negative square root of thirty six:<br />Square root of negative thirty six:<br />
15.
Exponents versus Indexes<br />When an exponent is not written, it is understood to be a one (like raising something to the first power)<br />When an index is not written on a radical, it is understood to be a two (as in a square root).<br />
16.
When a root is not a square root:<br />We used the “break-it-down” rule AND we had to know the meaning of that little three.<br />I know you can’t use calculators, but you’ll recognize some of these perfect squares and perfect cubes after some practice:<br />3x3x3=27 4x4x4=64 5x5x5=125<br />
17.
When are square roots not even REAL?<br /><ul><li>The odd root of a negative will be a negative real:
18.
The even root of a negative is “No Real Number.”</li></li></ul><li>On page 16ish, there is a list of properties pertaining to radicals. Here are a few of them in action:<br />
21.
Adding/Subtracting Radicals<br />In order to add or subtract radicals, they MUST be “similar” first. (The radical parts need to look the same.)<br />To me, this is reminiscent of how fractions must have similar denominators in order to be added or subtracted.<br />In order to try to make them similar, all you can do is try to simplify each radical.<br />
22.
Simplify all radicals first.<br />WHEN THE RADICALS ARE FINALLY THE SAME, WE CAN SMASH THEM TOGETHER! (8 OF THEM MINUS 9 OF THEM IS -1 OF THEM.)<br />
Be the first to comment