Let’s talk about powers and exponents. Unfortunately for this stickman superhero, we’re not talking about those kind of powers. When I say the word powers, I mean numbers that are expressed with exponents. Powers are numbers expressed using exponents,
Okay, so let’s look at this: thirty-two equals two times two times two times two times two. Or another way we write that is two to the power of five. Every power is made up of two components, the two here in the green is called the base and the five, the smaller number at the top of the base, is called the exponent that you see in yellow here. The components together are then called a power. Not only the is two to the fifth a power, it’s also something that we call exponential form. When we were working with exponents, the exponent tells us how many times to multiply the base by itself. So in our last example, the base was two and the exponent was five. That meant that we needed to take the base of two and multiply it by itself five times: two times two times two times two times two, which equals thirty-two.
So when we see seven to the fourth power, what does that mean? Our exponent here is four and the base is seven, so we know we’re gonna multiply seven by itself four times: seven times seven times seven times seven. There is a name that we use when we write out our exponents in the form like this; we call it standard form. In this case, seven to the fourth power is two thousand four hundred and one; seven to the fourth power equals two thousand four hundred and one. In here, you can see that seven to the fourth power we call a power, or we say that it’s written in exponential form. We have the standard form which is where we write seven as a product of seven times seven times seven times seven, and then the solution is there.
There’s one more thing we need to talk about, and that’s the words we use when we’re talking about powers. In the last example I called this seven to the fourth power. That’s the words I used, seven to the fourth power. But some powers are special, and we use different words. While it is true that this is five to the second power, we actually call it five squared. Anytime you’re dealing with powers and the exponent is two, that number is called “squared” just like our example here, five squared. The other special case power is when we have a power of three. Anytime we have a power of three we use the word “cubed”. So this one, four to the third power, we would say four cubed instead.
So let’s try and write these powers in standard form. Standard form means we wanna write these without their exponents. three to the fifth power looks like this, and five squared is written like this. And another example, we wanna write these values in exponential form. So let’s use exponents to simplify these values and write them as a base and an exponent. Here we have seven multiplied by itself three times, so that’s seven cubed. Ten is being multiplied by itself four times, and we write that as ten to the fourth power. Now you can go try out your powers and exponents powers for yourself.