9.17+Rules+of+exponents

e.g. y^2x y^4= y^6
===

"EXPONENTS ARE SHORTHAND FOR REPEATED MULTIPLICATION OF THE SAME THING BY ITSELF."

So, for an example, let's look at multiplying 7 three times: (7)(7)(7)=7x7x7--> or, by using exponents, we shorten it to: (7)(7)(7)=7^3---> so the exponent is 3, because we are multiplying 7 three times over!

So, now we that know what exponents look like, we should probably know what the terms are. The actually prosses of using exponents is known as "raising the power", the expont being the "power". So with the example 7^3---> the exponent (three) is the the power, so this example (7^3) is pronounced as "seven to the power of three" See? it all makes sense.

Okay, so we get what they look like, and we understand how to say them, let's look into the RULES...yippy!

SIMPLIFY

the example we'll choose is: (a^4)(a^5) so in order to simplify this equasion, we'll identify what the information is telling us. 1. a^4 means a to the power of 4, which is axaxaxa, a multiplied by itself, four times over. 2.a^5 means a to the power of 5, which is axaxaxaxa, a multiplied by itself, five times over. 3.so using this information, we 'expand' them to work out the simplified form:

(a^4)(a^5) --->(aaaa)(aaaaa) <span style="color: #a23dff; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 160%;">--->aaaaaaaaa <span style="color: #a23dff; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 160%;">--->a^9 <span style="color: #a23dff; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 160%;">see?! we've just learnt to simply!!

<span style="color: #ff00ff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 190%;">NOTE: we can only simply LIKE TERMS, such as the example above, we CANNOT simplify if the bases don't match e.g:

<span style="color: #ff00ff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 190%;">(a^4)(b^5)

<span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">OKAY GUYS!!!! <span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">I have a cool as trick up my sleave, that I think you should all know. ==<span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">In a multiplication sum including exponents -and the bases are the same, all you've gotta do is ADD the exponents to get the new power!! == <span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">EEAAZZYY! :)

<span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">example: (x^3)(x^2)=x^5 <span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">-> x^3= (x)(x)(x) and x^2= (x)(x) <span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">-> (x^3)(x^2)=(x)(x)(x)(x)(x)>x^5

<span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">BUT ﻿WHEN THE BASES ARE DIFFERENT, but the EXPONENTS ARE THE SAME:
<span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">combine the bases <span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">example: (a^2)(b^2) <span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">->(a)(a)(b)(b)>(a)(b)(a)(b)>(ab)(ab)>(ab)^2

<span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">﻿DIVIDING
<span style="color: #7d00ff; font-family: Georgia,serif; font-size: 120%;">do the OPPOSITE of multiplication and SUBTRACT the exponents if the bases are alike.

<span style="background-color: #00ff06; color: #7205ff; font-family: Verdana,Geneva,sans-serif; font-size: 120%;">Thanks guys, and good luck for EOY exams. You're all bright enough to get into a good class, so don't stuff it up. :)

<span style="background-color: #00ff06; color: #7205ff; font-family: Verdana,Geneva,sans-serif; font-size: 120%;">PEACE!