Q: x12{\displaystyle x^{\frac {1}{2}}} is actually the exact same thing as x{\displaystyle {\sqrt {x}}}. This is done similarly no matter what the bottom of the fraction is, so x14{\displaystyle x^{\frac {1}{4}}} would be the 4th root of x, also written as x4{\displaystyle {\sqrt[{4}]{x}}} . Roots are the inverse of exponents. For example, if you took the answer to x4{\displaystyle {\sqrt[{4}]{x}}} raised it to the fourth power, you would be back at x{\displaystyle x}, such as 164=2{\displaystyle {\sqrt[{4}]{16}}=2} can be checked as 24=16{\displaystyle 2^{4}=16}. Also for example, if x4=2{\displaystyle {\sqrt[{4}]{x}}=2} then 24=x{\displaystyle 2^{4}=x} therefore x=2{\displaystyle x=2} . x53{\displaystyle x^{\frac {5}{3}}} might look impossible, but it is easy if you remember how exponents are multiplied. Simply turn the base into a root, like a normal fraction, then raise the whole thing to the power on the top of the fraction. If you're struggling to remember this, think through the theory. After all, 53{\displaystyle {\frac {5}{3}}} really just equals (13)∗5{\displaystyle ({\frac {1}{3}})*5} For example:  x53{\displaystyle x^{\frac {5}{3}}} x53=x5∗x13{\displaystyle x^{\frac {5}{3}}=x^{5}*x^{\frac {1}{3}}} x13=x3{\displaystyle x^{\frac {1}{3}}={\sqrt[{3}]{x}}}  x53=x5∗x13{\displaystyle x^{\frac {5}{3}}=x^{5}*x^{\frac {1}{3}}} = (x3)5{\displaystyle ({\sqrt[{3}]{x}})^{5}} It is much easier to try and add and subtract your exponents before solving them or turning them into roots. If the base is the same and the exponent identical, you can add and subtract like normal. If the base is the same, you can multiply and divide the exponents like normal as well, as long as your remember how to add and subtract fractions. For example:  x53+x53=2(x53){\displaystyle x^{\frac {5}{3}}+x^{\frac {5}{3}}=2(x^{\frac {5}{3}})}  x53∗x23=x73{\displaystyle x^{\frac {5}{3}}*x^{\frac {2}{3}}=x^{\frac {7}{3}}}
A: Treat fractional exponents, like x12{\displaystyle x^{\frac {1}{2}}} like a square root problem. Turn the top number into a normal exponent for mixed fractions. Add, subtract, and multiply fractional exponents just like normal.

Q: S/he will examine the infected area and take an x-ray. to determine the severity of the situation and identify the best treatment.  S/he will examine the position of the tooth to see whether it has fully or partially emerged from the gums. Your dentist will also take note of the condition of the surrounding gums. If the wisdom tooth has not yet emerged, the dentist may need to perform an x-ray to locate the tooth and identify its position. These factors will influence whether or not the tooth will need to be removed. Don’t forget your medical history. Your dentist will want to know if you’re allergic to any medication. Consult with your dentist about how much the procedure will cost. You should also ask about all the risks and benefits of the treatment, as well as any alternative treatments that may be an option. Don’t be afraid to ask questions. You have the right to understand your medical care. If the wisdom tooth is about to emerge from the gums without any problems and the infection is not too severe, the dentist may be able to clear the infection by simply cleaning the area with an antiseptic solution.  The dentist will remove any infected tissue, pus, food debris or plaque from around the area. If there is an abscess on the gums, sometimes a small incision will be made to drain the pus. After the cleaning, your dentist will recommend home care for you to follow over the next few days. This might include mouth gels to bring down inflammation, antibiotics to fully clear the infection, and painkillers to relieve any pain. Commonly prescribed antibiotics include Amoxicillin, Clindamycin, and Penicillin. One of the main causes of wisdom tooth infection is when a section of gum covering the wisdom tooth — known as the gum flap —becomes infected due to bacteria, plaque and food debris becoming trapped underneath it. If the tooth is still buried within the gums (but is positioned to emerge from the gums correctly) it is often easier to remove the infected gum flap than the tooth itself.  Your dentist might schedule a minor surgical procedure called an ‘operculectomy’, in which the soft gum tissue covering the wisdom tooth is removed.  Once removed, the area will be a lot easier to keep clean and free of plaque and bacteria, which greatly reduces the chances of the wisdom tooth becoming reinfected. Before the procedure, your dentist will numb the area with a local anesthetic. S/he will then remove the infected tissue flap using surgical scalpel blades, lasers or electrocautery methods. If you have suffered from multiple infections and your wisdom tooth shows no sign of emerging on its own, it may be necessary to have the tooth removed. Extraction may also be necessary if the infection is very severe.  Depending on the position of the tooth, the extraction will be conducted by your dentist or by an oral surgeon.  The dentist will give you a local anaesthetic and will remove the tooth.  You may be prescribed antibiotics and painkillers to prevent further infection and relieve any pain. It is essential that you follow your dentist's advice regarding good oral hygiene practices. You will need to schedule a follow-up appointment with your dentist to inspect the gums to ensure they are healing properly. The dentist will check the positioning of the opposite wisdom tooth, in case it need to be removed also.
A:
Discuss the treatment with your dentist. Ask about costs, risks, and benefits of treatment. Let your dentist clean the infected area. Prepare yourself for minor surgery. Consider a tooth extraction.