Any value - we'll say "x" - raised to a negative power is equal to one divided by that value to the absolute value of that same power. In other words:
x-y = 1 / (xy)
The easiest way to see why this is true is to think of how you would get to a negative power. Consider:
x4 / x = x3
x3 / x = x2
x2 / x = x1 (or simply "x")
As you can see, each time we divide by x, the the exponent is decreased by one. This holds true no matter how many times you do it:
x1 / x = x0 (which is the same as saying "x / x = 1")
x0 / x = x-1 (which can also be expressed as "1 / x = x-1")
x-1 / x = x-2 (or, (1/x) / x = 1/(x * x) = 1/x2)
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You can have negative exponents anywhere. When they are in the denominator, they are equivalent to positive exponents in the numerator of a fraction.
by doing reciprocal
They are the reciprocals of the positive exponents. Thus, x-a = 1/xa
A negative exponent becomes positive in the reciprocal. So if you have a number a^x where x is negative, then, a^x = 1/(a^-x) and, since x is negative, -x is positive.
Put the number with the exponent in the denominator of a fraction and take off the negative symbol. The numerator in that fraction should be 1. Example: 8-2 Converts to: 1 --- 82