Simplify

(x^-6)-3

To simplify the expression (x^-6)-3, we first need to understand the concept of negative exponents.

A negative exponent indicates that the base should be moved to the opposite position in the fraction, either from the numerator to the denominator or vice versa. Specifically, if we have x^-a, where "x" is the base and "a" is the exponent, it can be rewritten as 1/x^a.

Now, let's apply this knowledge to the given expression:
(x^-6)-3

First, we'll rewrite x^-6 as 1/x^6:
1/x^6 - 3

Next, we need to simplify the expression further. Since there is no addition or subtraction in the denominator, we need to find the least common denominator (LCD) for the fractions.

Since the LCD of 1/x^6 and 3 is x^6, we can multiply the first term numerator and denominator by x^6 to get a common denominator:
(1/x^6)*(x^6/x^6) - 3

Simplifying:
x^6/x^6 - 3

The numerator, x^6, cancels out with the denominator, x^6, leaving us with:
1 - 3

Finally, we can subtract 3 from 1 to get the simplified result:
-2

Therefore, the simplified expression for (x^-6)-3 is -2.