Of cause we won’t rush to the rules of exponents without the knowledge of exponents themselves, so what is an exponent. It is a number raised to the other, representing the number of times that number is multiplied by itself.
Reading terminology:
The number can be read as an index or to the power of. For example, 2 index two, which is similar to 2 raised to two or two to the power of two. And that is 2x2, two to index 3 is 2x2x2; just like the definition expressed, the index represents the number of times the base is multiplied by the exponent.
Oh, so now there is a base, what now is a base of an exponent. The base is the number which is being multiplied by itself by the number of times represented by the exponent, from the above example 2 was used as a base and 3 as an exponent (23 , 2 is base, 3 is an exponent. This equals 2x2x2, that is the based 2 multiplied by itself 3 times, the number expressed by the exponent)
Now the rules:
Now that we understand what an exponent is, what are the rules then, why are they made, because they did not come out of thin air.
Law 1
Any number raised to 0 is equal to 1.
Law 2
Any number raised to a negative exponent,
Is equal to 1 over that number raised to that positive exponent
Law 3
When the same bases are multiplied,
What do we do? We add the exponents
And raise them to one base
Law 4
What if the same bases are dividing now?
We do what? We subtract the exponents
And raise them to one base
Law 5
It happens that an exponent is raised to the other,
When this is the case, we multiply the exponents by each other
Law 6
When two different bases are dividing,
In brackets and raised to one exponent,
We raise the numerator and denominator to that exponent
But why these rules?
Like I said, they did not come from thin air. These were made to simplify equations and expressions involving exponents with ease, you are expected to be able to solve such expressions without the use of a calculator and these rules make that very simple.
These rules don’t go allow, they have a friend over their shoulder taking the journey together, to where I don’t know. The good friend is called surds.
Surds:
I don’t know the official definition of this ones but they are simply numbers that can be expressed with the aid of a root. Not just a square root right, a root. There’s a difference.
Law 1
Any number raised to an exponent that is a fraction,
Is equal to the denominator root of
That number raised to the numerator.
Yes just like that, read it again if you have to.
Example: 21/3 = the cube root of 2 index 1
Law 2
When two numbers are multiplied inside a root,
They are equal the root of each number multiplied
Law 3
When a number is rooted to two numbers multiplied by each other,
Like 2 rooted to 4x3
That is equal to the 4th root of the cube root of 2
I hope you understand that, read it again if you have to, and use your study guide for furtherance.
Operating Disclaimer:
This blog post is not the first step towards learning the concepts of math but the coupling step to ease the use of your study guide and other study material. Read it over and over again to keep the concepts at the back of your head. Math is a subject of rules; know the rules, be able to duplicate them on a blank paper and go fetch your distinction.