What Do You Do When You Add Exponents

Hey there, math whiz! Ever found yourself staring at a problem, wondering, "What do I do when I add exponents?" Well, grab your coffee, 'cause we're about to dive in and make sense of this together.

First things first: what's the deal with exponents?

Exponents, my friend, are like little powerhouses. They tell us how many times a number (the base) is multiplied by itself. For instance, 2³ means 2 multiplied by itself 3 times, which equals 8. Easy peasy, right?

Now, let's talk about adding exponents.

When you see something like 3² + 2³, you might be tempted to just add the exponents together. But hold your horses! That's not how it works.

Here's the thing: you can only add exponents if the bases are the same. Let me repeat that, 'cause it's a game-changer. You can only add exponents if the bases are the same.

So, what do you do when the bases are different?

When you've got different bases, like in 3² + 2³, you can't add the exponents. Instead, you add the numbers themselves. That's right, you just add 9 (which is 3²) and 8 (which is 2³) together to get 17.

But what if you want to compare them? Well, that's a whole different story. You might need to convert them to the same base or use logarithms. But that's a conversation for another coffee break, yeah?

What about when the bases are the same?

When you've got the same bases, like in 2³ + 2⁴, you can add the exponents together. So, that's 3 + 4, which equals 7. And then you write it as 2⁷.

Do You Add Powers In Brackets at Gabrielle Pillinger blog

But remember, this only works when the bases are the same. If you try it with different bases, you'll end up with a mess. Trust me, I've been there. It's not pretty.

Let's not forget about zero and one.

Zero and one are special cases, my friend. Anything raised to the power of zero is 1. So, 3⁰ equals 1, just like 2⁰ and 10⁰. Easy, right?

And one? Well, anything raised to the power of one is just itself. So, 3¹ is 3, and 2¹ is 2. Simple as that.

So, what's the moral of the story?

When you're adding exponents, the key is to check the bases. If they're the same, add the exponents. If they're different, add the numbers themselves. And remember, zero and one have their own rules. Stick to these, and you'll be adding exponents like a pro in no time.

Now, who's ready for a refill? I feel like we've earned it.