ʕ•ᴥ•ʔ Simplify Expressions with Ease using the Exponent Rules

We have now learned all individual exponent rules in the previous sessions. In this session, we will try to use different exponent rules to solve problems.

Hi, welcome to this question here. Well, this one looks a very, very hard question but it's actually not. See, what we have to remember is actually the order of operations which is called the PEMDAS, right? You want to do what's in the brackets first. So, let's not worry about the 3 on the outside first, let's just kind of consider what is happening inside, everything here is multiplying and dividing, we've got an "a" and "b", it's just "a" and "b" with some numbers in the front. So, let's deal one thing at a time.
So here we go, let's have the bigger brackets on the outside so just to remind ourselves that we're gonna do the power of 3 at the very end, OK? So, I have a negative 16, I've got a 3, I've got a 2. So, that means we will still have a negative, OK? 16 and "a", we're gonna do a quick reduce right there and that's gonna be an 8 right there. And 8 times 3 gives you, 24. So, let's put 24 there and we're done with all the coefficients, then let's do the "a". That's a 5 and that's a 3, these guys are multiplying so you add exponents. So it's 8 so far, and there's a 2 down here, with the same base of "a", right? This is all the same base, you can actually just deal with the exponents. So, we've got a 5 plus 3, 8. Subtracted 2, it's 6. So, it's a to the power of 6. Does that make sense?
Then we've got a "b". Again, they have the same base here and here and here. Negative 3 multiplying, so we've got to do negative 3 plus the 5, which is 2 and then 2 minus negative 2. So, it's gonna give you a 4. I'm gonna get a "b" to the power of 4 right here. And guess what? That's it. That's basically what happens in the inside here. It's just that and we have to raise it to the power of 3.
The power of 3 just kind of multiplies to everything. The negative to the power of 3 is still negative, OK? The 24 to the power of 3 is such a big number that we can actually leave it as it is, or you can actually simply punch it in the calculator and you get the answer for that. So, it's 13824 and we can do "a" to the power of 6 to the power of 3 we've got an 18 right there. And then we've got a 4 and 3, and that's that. Hopefully, that's correct, OK? So, that's the final answer. Nice and easy, right? Thanks for watching.

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