explain how to do exponents and variables

Question

I was never able to grasp how to do it. I just need directions how to do this

Answer 1

A variable is a number whose value you may not know. Think of it as a paper cup with a number inside it that you can't see; on the outside someone has written a name on the cup, like x or y or f(x).

 

You use algebra to manipulate equations to get a variable on one side by itself and a number whose value you know on the other; then you infer that the value inside the cup is the same as the numbers on the other side of the equation.

 

When you add a lot of the same number together you can replace the sum with the number times the number of them you added; e.g., 2+2+2 = 2*3.

 

Exponents are similar. When you multiply a lot of the same number together you can replace the product with the number raised to the number of them you multiplied; e.g., 2*2*2 = 2^3.  (Note that * means multiply.)

 

In both cases we're defining some shorthand way of expressing an otherwise verbose expression.

 

If you graph y = 2^x for integer values of x you will get a set of points.

 

And you will want, I hope, to try to connect the points with a smooth curve. When you do that you've just indicated that exponents can be all real numbers, not just integers. And from your graph you can estimate the value of, say, 2^pi; or 2^(any real number).

 

Then there are rule for manipulating exponents:

 

a^m * a^n = a^(m+n)

a^m / a^n = a^(m-n)

(a^m)^n = a^(m*n)

 

+ more that your teacher will help you with.