Using the symbol "^" for power:
a^(-b) = 1 / (a^b)
and:
a^b = 1 / (a^(-b))
In words: raising a number to a negative power is the reciprocal of the same number, raised to the corresponding positive power (the additive inverse).
3
You can have negative exponents anywhere. When they are in the denominator, they are equivalent to positive exponents in the numerator of a fraction.
why the exponents can not be negative
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.
by doing reciprocal
Exponents that are NOT a negative exponent therefore they are mostly whole numbers kind of:)
They are the reciprocals of the positive exponents. Thus, x-a = 1/xa
To eliminate negative exponents, you can rewrite the expression using positive exponents. Specifically, if you have a term like ( a^{-n} ), you can convert it to ( \frac{1}{a^n} ). This means that any base with a negative exponent can be moved to the denominator of a fraction, turning the exponent positive.
Positive exponents: an = a*a*a*...*a where there are n (>0) lots of a. Negative exponents: a-n = 1/(a*a*a*...*a) where there are n (>0) lots of a.
Exactly that ... negative exponents. For example: 1000 = 103 That is a positive exponent. .001 = 10-3 That is a negative exponent. For positive exponents, you move the decimal place that many positions to the right, adding zeros as needed. For negative exponents, you move the decimal place that many positions to the LEFT, adding zeros as needed. And, the special case is this: 100 = 1.
They can be written as reciprocals with positive exponents. For example, 5-7 = (1/5)7
Exactly that ... negative exponents. For example: 1000 = 103 That is a positive exponent. .001 = 10-3 That is a negative exponent. For positive exponents, you move the decimal place that many positions to the right, adding zeros as needed. For negative exponents, you move the decimal place that many positions to the LEFT, adding zeros as needed. And, the special case is this: 100 = 1.