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. 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. Notice how that negative sign no longer shows up. The 2nd condition: 'Fractional exponent must be in simplest form. This can also be proved in calculus, and the fact that ar er ln a a r e r ln a. 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. The 1st condition: 'The laws of exponents still apply to fractional exponents.' This condition is true, since a fractional exponent is still an exponent. 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. I am still not sure, if this works in every case, but for me it. 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. With this expressions with negative exponents are always output as fractions. Negative baseĬomputing a negative exponent with a negative base is very similar, and just requires us to remember the rule that a negative base raised to an even exponent results in an even number, while a negative base raised to an odd exponent results in an odd number.As you guys know there's lots of properties and shortcuts you can use when working with exponents. The 2nd condition: 'Fractional exponent must be in simplest form.' Lets say you have a negative number (e.g. In the x case, the exponent is positive, so applying the rule gives x (-20. In the case of the 12s, you subtract -7- (-5), so two negatives in a row create a positive answer which is where the +5 comes from. We know that b -m = 1/b m, so we can move the b m to the numerator by taking the reciprocal, then adding a negative sign:īelow are a few examples of computing negative exponents given different cases. The rule for dividing same bases is xa/xbx (a-b), so with dividing same bases you subtract the exponents. We can see that this aligns with the formula above since 2 -5 = 1/2 5.Īnother way to confirm this is using the property of exponents that states: In contrast, a negative integer exponent can be computed by multiplying by the reciprocal of the base, n times. It is important to remember that as we simplify with fractional and negative exponents, we are using the same properties we used when simplifying integer. For example, given the power 2 5, we would multiply 2 five times: Since d-3 on the bottom has a negative exponent, it is moved to the. Briefly, a positive integer exponent indicates how many times to multiply by the base. The top and bottom both contain negative exponents.
Refer to the following pages for other exponent cases or rules. This is the equivalent of taking the reciprocal of the base (if the base is b, the reciprocal is b -1 = ), removing the negative sign, then computing the positive exponent as you would normally. In other words, a negative exponent indicates the inverse operation from a positive integer exponent: it indicates how many times to divide by the base, rather than multiply. Home / algebra / exponent / negative exponents Negative exponentsĪ negative exponent is equal to the reciprocal of the base of the negative exponent raised to the positive power.
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