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)
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
You can have negative exponents anywhere. When they are in the denominator, they are equivalent to positive exponents in the numerator of a fraction.
Negative exponents are used to represent 1 divided by an a base to a specific exponent.
why the exponents can not be negative
When multiplying numbers with exponents, you add the exponents.
by doing reciprocal
3
They are the reciprocals of the positive exponents. Thus, x-a = 1/xa
Exponents that are NOT a negative exponent therefore they are mostly whole numbers kind of:)
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.
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.
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.