LAWS OF EXPONENTS PART 1

Yes we can expand any variable with an exponent, except a variable that has an exponent of one.
The exponent of y is one. x*x equals x^2.It equals x^2 and not just x because when you multiply a number or variable by itself, the number or variable then becomes squared. A pattern I noticed when I multiply exponents is that you can just add the exponents, which is what the Laws of Exponents says.

LAWS OF EXPONENTS PART 2

Since I am explaining the laws of exponents to a 3rd grader, i will have to explain this in simplest form.Now, the laws of exponents state that when you multiply a number with the same variable (an unknown value), you can add the exponents. Exponents are the little numbers above the variable,(letter). The exponent shows how many times the letter will be multiplied by itself. It looks like this, a^2. So for example, a^2 * a^2= a^4.Now, the laws of exponents also state that when you divide a number with the same variable, you can subtract the exponents. For example a^2 / a^2=a.

Integral Exponents

To square a number is to multiply a number by itself.To cube a number is to multiply a number by itself three times.An integral exponent is a positive or a negative exponent.

UNLIKE TERMS

Yes, x is different from x2 because x is alone,there's no operation. In x2 there is an operation, (multiplication). We can combine terms with the same exponents. They would be called like terms. You can remember that subtracting a large number from a small number will equal a negative number. Yes, 8m-2m is the same as 8m+ -2m. They are the same because 8m-2m=6m, and 8m+ - 2m=6m. Coefficients are numbers that show how many times a variable will be multiplied. Coefficients are always next to the variables.Coefficients are important because those are the numbers that you are combining.

Like Terms

My definition of like terms is that like terms are terms with the same variable and exponent.
100p and 3000p are like terms.I can combine them because they have the same variable and exponent. p and p2 are not like terms they have the same variable but not the same exponent,
therefore you cannot combine them. We cannot combine 2d and 2f because they do not have the same variable or exponent. An expression cannot have an equal sign because you cannot combine unlike terms. You can only simplify an expression. Unless all of the terms are alike. A perimeter
is the distance around an object.

Moving Variables

We move one variable term to the other side of the equal sign by doing the inverse operation.
Yes we would have to add 4j to 16j in the problem 16j=12-4j because 4j and 16j are like terms.
Therefore you do have to use the inverse operation. The relationship between subtraction and addition is that addition is the inverse operation of subtraction.Their like brother and sister.
The phrase ''what we do to one side we must do to the other'' relates to a balance scale because
by doing something to one side and doing the same to the other your making both sides equal and
a scale is used to tell whether both sides are the same.