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Rewrite the following expression as the product of positive exponents, and then evaluate

2
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the expression when x=2.

3
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So they give us x to the negative 3 times 5 to the negative 2 times

4
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x squared.

5
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So the main thing to realize here is if I had something to a negative

6
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exponent, this is the exact same thing as 1 over that same base,

7
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to the positive version of the exponent.

8
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So x to the negative a is equal to 1 over x to the a.

9
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So using this knowledge just supply it over here.

10
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So x to the negative 3,

11
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power,

12
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We can rewrite as 1 over x to the third power.

13
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And then 5 to the negative 2, we can rewrite as 1 over 5 squared.

14
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And then finally we have times x squared.

15
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So we can multiply this out and the numerator we have 1 times 1 times x squared.

16
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Which is just equal to x squared.

17
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And the denominator we have x to the third times 5 squared.

18
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5 squared is 25, and here you could say implicit there is a 1.

19
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This is the same thing as x squared over 1.

20
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So the denominator we have 25 times x to the third.

21
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So this is going to be 25, times x to the third.

22
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And then we can simplify this even more because

23
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both the numerator and the denominator is divisible by x squared.

24
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x squared divided by x squared is 1.

25
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x to the third divided by x squared is just going to be equal to x.

26
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And you can use other exponent properties

27
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you can say x squared over x to the third is the same thing as

28
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x to the 2 minus 3 power which is x to the negative 1 power,

29
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But x to the negative 1 power we know it is the same thing as 1 over

30
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x.

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Any way you do it as long you do it any reasonable way,

32
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you should get the same result.

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So when we simplify it,

34
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we get 1 over 25 x.

35
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Now, they want us to evaluate it when x=2.

36
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So if x is equal to 2, we get 1 over 25 times 2 which is equal to 1

37
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over

38
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50. And we are done.

39
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We rewrote the expression as a product of positive exponents.

40
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That's right over here.

41
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We made all the exponents positive.

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And then we evaluate it.

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We got 1 over 50.