Exponents

What is an exponent?

An exponent is the lazy way of saying, "multiply something against itself a bunch of times."

a*a*a*a*a = a^5 (there were 5 a's so the exponent is 5)

See isn't that shorter?

But along with writing something shorter, you have to learn to use the notation.

Let's learn how you deal with

a^3 * a^4

In long hand that is:

a*a*a * a*a*a*a = a^7

So in other words

a^3 * a^4 = a^(3+4)

Generically that is:

a^x * a^y = a^(x + y)

Multiplying a terms with similar variables, means you need to ADD exponents.

Now let's look at negative exponents.

1/a * 1/a * 1/a = = 1/(a*a*a) = 1/(a^3)

If we look at this example

(a^5)/(a^3) it looks like this in long form:

(a*a*a*a*a)/(a*a*a) = a*a = a^2

So in other words:
a^5/a^3 = a^(5 - 3) = a^2

Dividing terms with similar exponents, is the same as SUBTRACTING the exponents.

Generally speaking:
a^x/a^y = a^(x-y)

Now for the fun part!

If x is smaller than y, the exponent would be NEGATIVE!

a^3/a^5 = a^-2 = 1/a^2

So what does it mean if the exponent is zero????

Let's look at this example.

a^x/a^x = 1
a^(x - x) = 1
a^0 = 1

And that is true for ANY a!