Zero and Negative Exponents - Concept
It's important to understand what It means to have negative exponents and zero exponents. Negative exponents put the exponentiated term in the denominator of a fraction and zero exponents just make the term equal to one. We can use negative exponents for cancelling with positive exponents while solving equations or simplifying expressions, although we need to keep in mind the rules of multiplying exponents.
As you guys know there's lots of properties and shortcuts you can use when working with exponents. One property meaning it's always true about exponents, is that any number to the zero exponent give you an answer of 1, it might be the letter x, it might be 5, it might 800 anything. I can even write 800 to the zero equals 1, I could write clouds, smiley cloud to the zero power whatever I have in there, anything to the zero power gives me equivalent statement of 1. That's something to keep in mind, it shortens a lot of your problems with exponents.
Another thing to look out for is a negative exponent, if you have x to the negative m that's equal to 1 over x to the positive m. Notice how that negative sign no longer shows up. This will might also show up in a different way if for example you had x to the negative m in the denominator of the fraction, that negative means it's going to become x to the positive m on top of a fraction like that. The negative kind of you can think of changing places in the fraction. If it's in the bottom, it moves to the top, if it's in the top, it moves to the bottom. And the new exponent will be no longer negative it will become positive.
Although there are some properties there's no real shortcuts with these guys, these little ones you just kind of have to memorize and get into your brain when it comes to doing your exponent homework. Anything to the zero power equals 1 and the negative becomes positive when you change where it shows up in the fraction.