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If x y = (x

^{2}– 3)/ y^{x}for all x and y, then what is the value of -1 5?Correct Answer:

**A**- The operation defines for us what to do with any two numbers, one of which is to the left of the operation and the other of which is to the right. Because both x and -1 are to the left of the operation , we may replace x with -1 every time we see x. Because y and 5 are to the right of operation , we can replace y with 5 every time we see y.
- Plugging in -1 for x and 5 for y, we get -1 5 =

- We can determine the numerator first. (-1)
^{2}= 1, because -1 * -1 = 1. Then we take 1 – 3, which is -2. So the numerator equals -2. - For the denominator, when you see a negative exponent, use the inverse of the base (1 over the base) and raise this number to the positive form of the exponent. For example, 2
^{-3}is 1/ 2^{3}. Here we have 5^{-1}, which is the same as 1 / 5^{1}, or 1/5, because any number to the power of 1 is the number itself. - Putting the numerator and denominator together, we have:

= -2(5/1) = -10

Note: when you divide by a fraction, it is the equivalent of multiplying by the inverse of the fraction.- Answer choice A is correct.