Order of operations examples: exponents

So I have six different expressions here, and what I want you to do is pause this video and try to calculate the value of each of these expressions. I'm assuming you've given a go at it. Now let's work through them. So when we see something like this, we have to remember our order of operations. We have 2 times 3 squared, and we have to remember that the first thing we would need to think about are the parentheses. I'll just write paren for short. Then we worry about exponents. Then we will worry about multiplication and division, and actually let me write it this way. We worry about multiplication and division. And then we worry about addition and subtraction. So in this expression right over here, there are no parentheses, so we do the exponents first. So we calculate what 3 squared is. 3 times 3 is 9, so this becomes 2 times 9, which is equal to 18. Now let's look at this one, and this one is interesting, because they have-- it looks like the same expression, but now there are parentheses. And because of these parentheses, we're going to do the multiplication before we take the exponent. So 2 times 3 is going to be 6, and we're going to take that to the second power. So that's 6 times 6, which is equal to 36. Now let's think about this one right over here. Once again, we want to do our multiplication and our division first. So we have a division right over here. 81/9 is the same thing as 81 divided by 9, and that's going to be 9. And then we have-- so it becomes 1 plus 5 times 9. Now we want to do the multiplication before we do the addition, so we're going to do our 5 times 9, which is 45. So this becomes 1 plus 45, which of course is equal to 46. Now let's tackle this one right over here. So, we would want to do the exponents first. So, 1 squared, well that's just going-- let me do this in a different color. 1 squared is just going to be equal to 1, so that's just going to be equal to 1. And so you have 2 times 4 plus 1. What should you do? Should you add first or do the multiplication first? Well multiplication takes precedence over addition, so you're going to do the 2 times 4 first. 2 times 4 is 8, so you're going to have 8 plus 1, which of course is equal to 9. Now you have a very similar expression, but you have parentheses. So that's going to force you to do what's in the parentheses before you take the exponent. But within the parentheses we have multiplication and addition, and we have to remember that we do the multiplication first. So we're going to do the 2 times 4 first, so that's going to be 8 plus 1 to the second power. 8 plus 1 is 9, so that's 9 to the second power. 9 squared is the same thing as 9 times 9, which is equal to 81. Now we have one more right over here that looks very similar to this one, except, once again, we have parentheses that's making us do the addition first. Without parentheses, we would do the multiplication and the division first. But here, we see that 1 plus 5 is 6, and then we have this 81/9, which is 9. So this simplifies to 6 times 9, which of course is equal to 54.