What Is An Exponent?

An exponent is the amount of times a number is being multiplied by itself. If you have a number like 3 to the power of the then you solve it by going 3 x 3 x 3. which makes it 9 times 3 and thats 27. 1 power is essentially just a copy of the number. exponents are good because you can use them to make your equation a lot smaller then it actually is. Like if you had 10 to the power of 4 it doesn’t sound that big but it is actually 10,000.

What Is The Difference Between Evaluating and Simplifying?

The difference between simplifying and evaluating is that when you simplify, you use one of or all 3 of the different exponent rules. The Power Law, The Multiplication Law, and the Division Law. Evaluating is when you actually solve the equation and the exponent. Like if it had 8 to the 4th power you would have to figure out what number that equals to.

Multiplication Law and How It Works

The multiplication law is quite simple.  An example would be if you had 4 to the 6th power times 4 to the 3rd power. This question would be alot more difficult if you had different bases, but since they are the same all you have to do is add the exponent numbers. Since there was a 6 and 3 you just add the two together and your answer would be 4 to the 9th power. If you wanted to do this but with 2 negative numbers it would work exactly the same because the only thing that matter when doing this rule is that the bases are identical.

Division Law and How It Works

The division law is just as easy to learn and understand as the multiplication. It works the exact same way except instead of adding the exponent you would subtract them. For example 8 to the 9th power divided by 8 to the 3rd power. Since both bases are the same you just subtract 9-3 and you are left with 8 to the 6th power. One strategy we learned was we draw all of the exponents from the first number so from my example we would draw 9 eights. Then we draw on a line below the subtracted amount which was 3 eights, then we just subtract the amount of 8s and are left with number that goes in the power spot.

The Power Law and How It Works

the power law is when you have an equation that has a number on the inside of brackets with an exponent and the outside of the bracket also has an exponent. For example we can do ( 4 to the 3rd power) to the 4th power. what you do in that case is multiply the inside power and the outside power so in that circumstance you would have 4 to the 12th power. The nice thing about this law is even if the base is negative all you have to do is continue doing the question like normal and keep the negative base where it was.

Applications of Exponents

One time that you would be applying exponents to other things is with the pythagorean theorem. what you do is a squared + b squared = c squared.  As an example lets say A = 4m  B = 5m C=?m what you do is square A which is 16. Then you square B which is 25. Then you add the 2 together which leaves you with the sum of 41. Then you find the square root of 41 which is 6.403m so the length of A = 4 B = 5 C = 6.403.

One More Thing I Have Learned About Exponents

One other thing i have learned about exponents is that whenever there is a number to the power of 0 then the real value of that number is 1. The other thing i learned or i guess more realized is that every singe number has an invisible power of 1 but it just isn’t shown