![]() Anything to the zero power equals 1 and the negative becomes positive when you change where it shows up in the fraction. And the new exponent will be no longer negative it will become positive.Īlthough 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. If it's in the bottom, it moves to the top, if it's in the top, it moves to the bottom. The negative kind of you can think of changing places in the fraction. Rule 2: The rule holds true even when the denominator contains a negative exponent. Power rule (positive integer powers) Power rule (negative & fractional powers) Power rule (with rewriting the expression) Power rule (with rewriting the expression) Justifying the power rule. Specifically, a ( n) 1 a × 1 a × n times which equals 1 an. ![]() In technical terms, the 'minus' in the power means that you should convert the base expression to its reciprocal. Rule 1: The reciprocal of a base, which is 1 a, is multiplied by itself n times according to the negative exponent rule for bases with the negative exponent n. A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. 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. Once you've learned about negative numbers, you can also learn about negative powers. Notice how that negative sign no longer shows up. That's something to keep in mind, it shortens a lot of your problems with exponents.Īnother 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. 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. 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. As you guys know there's lots of properties and shortcuts you can use when working with exponents.
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