1
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Simplify x to the third, and then that raised to the 4th power times x squared, and then that raised to the 5th power

2
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Here we'll use the power property of exponents, sometimes called the power rule.

3
00:00:15,000 --> 00:00:26,067
And that just tells us if I have x to the a and then I raise that to the bth power, this is the same as x to the a times b power.

4
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To see why that works, let's try that with the - well I won't do that with these right here - I'll do it with a simpler example.

5
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let's say we are taking x squared and raising that to the third power.

6
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Well in that situation, that literally means multiplying x squared by itself, three times.

7
00:00:42,975 --> 00:00:52,575
So that literally means, x squared times x squared times x squared. I'm taking x squared and raising it to the third power.

8
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Now what does this mean over here? Well, there's a couple of ways to do it. You could just say ... like, I have the same base, I'm taking the product ... so I can just add the exponents.

9
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So this is going to be equal to - let me do it in that same magenta - x to the two plus two plus two power ... or essentially x to the three times two.

10
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This right here is just 3 times 2, So we get x to the 6th power.

11
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So you say "hey sal, I don't see why you can add those exponents..."

12
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Well, this over here we can write as x times x, times x times x, -- In parentheses I'm putting each of these x squareds.-- times x times x.

13
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And this is just x times itself 6 times, or x to the 6th power. This is why we can add the exponents like that.

14
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So let's use this powers of exponents property on this expression right over here.

15
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To start off we have x to the third raised to the fourth power.

16
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So that's just going to be x to the three times 4 power.

17
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or x to the 12th power.

18
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Then we muliply that by x squared raised to the fifth power

19
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well that's just going to be x to the 2 times 5 power, or x to the tenth power.

20
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And now that we have the same base, and we're taking the product, we can just add the exponents

21
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This is going to be equal to - this whole expression is going to be equal to x to the 12 plus 10th power, or x to the 22nd power.

22
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And we are done!