Help with my algebra!! Simplify Expression!!?

You just add the exponents when multiplying. X^12 * X = X^13.

x^12 basically means x written 12 times. As stated already above it is in other words, xxxxxxxxxxxx (that's 12 Xs.)

x is written as x^1. In other words, it is x written once.

The rule is if your multiplying the same variables, the variable stays the same and you add the exponents.

First let's forget about the exponents for each variable. You are left with x times x. x times x is not 2x (that would be adding variables). Since you are multiplying, x does change. x will forever stay as x. x is basically 1x so you are technically doing 1x times 1x. Because it's 1 times 1 and x stays the same, the answer is x. If for example, it was 2x times 3x, then the answer is 6x because you multiply 2 and 3 and leave x as it is, it does not suddenly turn into another variable.

Secondly, add the exponents. So the exponents were 12 and 1. (x is not x^0, it x^1). 12 +1 is 13.

Therefore the total variable is x and the total exponent is 13 and thus it is written as x^13.

x^12 is like saying x*x*x*x*x*x*x*x*x*x*x*x

or x multiplied by itself 12 times, adding another x:

x*x*x*x*x*x*x*x*x*x*x*x*x

would be multiplying x by itself 13 times, thereby making the simplified form of x^12 * x to be

x^13

x^13.