### Powers and exponents (Pre-Algebra, Discover fractions and factors) – Mathplanet

Adding and subtracting with exponents can be quite easy once you know They have the power to simplify repeated multiplication so we can. If two powers have the same base then we can multiply the powers. When we multiply When we divide powers we subtract their exponents. The rule: x a x b. The laws of exponents and radicals, and how to remember them. Except in one case: If the bases are different but the exponents are the same, bases you subtract exponents, just as for multiplication of like bases you add.

A coefficient appears before a variable in an expression and is multiplied by that variable. Let's take a look at the following expression: Hopefully you recognize that the base is x and the exponent is 5.

But, what is different from the terms we saw earlier in the lesson? This term now also has a coefficient of 2. Let's look at one more to make sure it makes sense. Can you identify the base, exponent, and coefficient? By the way, if there is no number before the variable or symbol, then the coefficient will be 1.

### Exponential and logarthmic functions | Khan Academy

The same is true if you don't see an exponent. Therefore, the term y would have a coefficient of 1 and an exponent of 1; they just do not need to be written, which simplifies things a bit. Here is another example: Now, we can move on to some simple rules so we can finally start adding and subtracting terms with exponents. Adding and Subtracting with Exponents When dealing with numbers only, we look at each expression, calculate, and then add or subtract as needed. Subtracting with exponents works the same way.

Different rules apply when dealing with variables. In order to add or subtract variables with exponents, you need to have like bases and like exponents, which means that the bases and exponents are the same. It does not matter if the bases are letters or even symbols; they need to be alike to be added or subtracted, and the exponents need to match.

For example, we can add and subtract the following expressions because they have like bases and like exponents: So that will give us Now I will ask you a more interesting question.

What do you think 2 to the negative 4 power is?

And I encourage you to pause the video and think about that. Well, you might be tempted to say, oh maybe it's negative 16 or something like that, but remember what the exponent operation is trying to do.

One way of viewing it is this is telling us how many times are we going to multiply 2 times negative 1? But here we're going to multiply negative 4 times. Well, what does negative traditionally mean? Negative traditionally means the opposite. So here this is how many times you're going to multiply. Maybe when we make it negative this says, how many times are we going to, starting with the 1, how many times are we going to divide by 2?

So let's think about that a little bit. So this could be viewed as 1 times, and we're going to divide by 2 four times.

## Negative exponents

And so you probably see the relationship here. If you're-- this is essentially you're starting with the 1 and you're dividing by 2 four times. Let me color code it nicely so you realize what the negative is doing. So this negative right over here-- let me do that in a better color, I'll do it in magenta, something that jumps out.

So this negative right over here, this is what's causing us to go one over. So 2 to the negative 4 is the same thing, based on the way we've defined it just up right here, as reciprocal of 2 to the fourth, or 1 over 2 to the fourth.

**Expanding Exponents with Different Bases (Simplifying Math)**

Or if you use this idea right over here, you could view it as starting with a 1 and multiplying it by 2 four times. So let's do a few more examples of this just so that we make sure things are clear to us.

So let's try 3 to the negative third power.

So remember, whenever you see that negative, what my brain always does is say I need to take the reciprocal here.