Exponents are simply a more organized was to write multiplication. Exponents are written as a variable in the top right corner above another variable. The terms we use to describe these terms are “Power” (Top part); and “Base” (Bottom part). In computer notation they may also be written with a caret symbol ^ due to lack of a high quality display. In this notation you would have the (Base)^(Power). Now that we have a basic way to describe an exponent let’s look at some examples.
8*8 = 8^2
In exponent notation this would be expressed as 8^2. This is because it is 8 times itself two times. So we take our base (8) and raise it to the 2nd power. Some may think what is the point of writing out 8^2 when 8*8 is just as easy to write. This is because in some circumstances our multiplication will not be so simple and we need a very precise and thorough way to describe it. For example if we had 8*8*8*8*8*8*8*8*8*8 this would be really daunting to write over and over again and it is much easier to write 8^10; because it is simply 8 times itself ten times.
5*2*5*3*2*8*5 = 5^3*2^2*3*8
This is a little more of a challenge but just like before we will take groups of the same number and raise the base number to a power that is equal to the number of times it is multiplied. From above we can see that we are multiplying 5 three times; 2 two times; 3 once; and 8 once. This means we will raise our bases to their respective powers while multiplying all of the bases together.
x*x=x^2
In any mathematics past algebra, one may find that not always are the bases and exponents numbers. We may see equations that have x^2; or 3^x ; or even (x-6)^(2+x). These may seem much more complicated than our previous problems but if we remember how exponents work we can simply think of them in a less ‘scary’ form like x*x; 3 times itself x amount of times; or (x-6) times itself (2+x) amount of times. Exponents are just useful ways to describe things and make multiplication work easier for us by hand and by calculator. Exponents even open up a world of rules and laws that even further build more advanced mathematical theories; but for now just consider them as a useful tool to help you do your multiplication.
