Jose S. | Friendly Mathematics, Philosophy, and Computer Science tutorFriendly Mathematics, Philosophy, and Co...

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Hey Carlos

You need to think about the rules for exponents. Is there any that tells you how to deal with negative exponents?

Here is a way to think about it. For positive exponents you could write x^n = x*x^(n-1), as long as n is greater than 0. This can be rewritten as: x^(n-1) = (x^n)/x, as long as x is not 0. Now suppose n is 0, and the rule gives us: x^(-1) = x^(0)/x. Since x^0 is 1, this means x^(-1) = 1/x. If we assume this holds as long as n is an integer(positive or negative) and x is not 0, then we have that x^(-2) = x^(-1)/x = ([x^0]/x)/x =(1/x)/x = 1/x^2, and in general x^(-n) = 1/(x^n). Then in your case, 4^(-4) = 1/(4^4).

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