Raising a number to a negative exponent gives you the reciprocal of the same number raised to the corresponding positive exponent. For example, 32 = 9, so 3-2 = 1/9
why the exponents can not be negative
When multiplying numbers with exponents, you add the exponents.
property of negative exponents
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.
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.
You can have negative exponents anywhere. When they are in the denominator, they are equivalent to positive exponents in the numerator of a fraction.
Monomials can have negative exponents, if the term for the exponent is not a variable, but if it is a variable with a negative exponent, the whole expression will not be classified. This is so because the definition of a monomial states that, a monomial can be a product of a number and one or more variables with positive integer exponents. I hope that answered your question!
Negative exponents are used to represent 1 divided by an a base to a specific exponent.
why the exponents can not be negative
Negative exponents indicate that the number for which the exponent applies to should be placed under one. Ex: 2^(-3) also can be expressed as 1/(2^3) or 1/8. So, to eliminate the negative exponent, simply place the number (and the accompanying exponent) under one to make a fraction.
When multiplying numbers with exponents, you add the exponents.
by doing reciprocal
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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
property of negative exponents
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.