So the question is "why is a number raised to a negative power always less than one, but not ever less than zero. Well negative exponents are a confusing topic, but I will try my best to explain them. There are different ways to solve a problem with negative exponents, but this is how I was taught. All that you have to do is first find the reciprocal of the number. So if you have 4^-2 you would change 4 to 1/4 and negative 2nd power to positive 2nd power, and now have 1/4^2. So then you just multiply 1/4 by itself and you get .0625 which is less than one, but not less than zero. This is actually a very simple method and the good thing is that it will work with any and every problem that has a negative exponent.
An exponent is a number placed after and above another number that shows the power of that number, or how many times you use that number in a multiplication. So if it says 2^3 it means that you have to do 2x2x2 which is 8. And if it says 8^4 you multiply eight by itself four times, which equals 4096. So that is basically how exponents work. Also, if you see exponents in a long problem where you have to use the order of operations, exponents would be the second operation you do after parentheses only. It is the "E" in PEMDAS, if you have always wondered about that like I did until I found out that it meant exponents. So for example if you had the expression 3+2-2^3+(4-2)=, you would first do what is inside the parentheses, which equals two. So now you have 3+2-2^3+2. Next you solve the exponents, 2^3, which is 8, so you now have 3+2-8+2=. Then you just finish the problem by working left to right. So now you know how exponents work, and what to do when you see them in a problem with order of operations.
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