Article: To convert a decimal to a fraction, consider place value. The denominator of the fraction will be the place value. The digits of the decimal will equal the numerator. For example, for the exponential expression 810.75{\displaystyle 81^{0.75}}, you need to convert 0.75{\displaystyle 0.75} to a fraction. Since the decimal goes to the hundredths place, the corresponding fraction is 75100{\displaystyle {\frac {75}{100}}}. Since you will be taking a root corresponding to the denominator of the exponent’s fraction, you want the denominator to be as small as possible. Do this by  simplifying the fraction. If your fraction is a mixed number (that is, if your exponent was a decimal greater than 1), rewrite it as an improper fraction. For example, the fraction 75100{\displaystyle {\frac {75}{100}}} reduces to 34{\displaystyle {\frac {3}{4}}}, So, 810.75=8134{\displaystyle 81^{0.75}=81^{\frac {3}{4}}} To do this, turn the numerator into a whole number, and multiply it by the unit fraction. The unit fraction is the fraction with the same denominator, but with 1 as the numerator. For example, since 34=14×3{\displaystyle {\frac {3}{4}}={\frac {1}{4}}\times 3}, you can rewrite the exponential expression as 8114×3{\displaystyle 81^{{\frac {1}{4}}\times 3}}. Remember that multiplying two exponents is like taking the power of a power. So x1b×a{\displaystyle x^{\frac {1}{b}}\times a} becomes (x1b)a{\displaystyle (x^{\frac {1}{b}})^{a}}. For example, 8114×3=(8114)3{\displaystyle 81^{{\frac {1}{4}}\times 3}=(81^{\frac {1}{4}})^{3}}. Taking a number by a rational exponent is equal to taking the appropriate root of the number. So, rewrite the base and its first exponent as a radical expression. For example, since 8114=814{\displaystyle 81^{\frac {1}{4}}={\sqrt[{4}]{81}}}, you can rewrite the expression as (814)3{\displaystyle ({\sqrt[{4}]{81}})^{3}}. Remember that the index (the small number outside the radical sign) tells you which root you are looking for.  If the numbers are cumbersome, the best way to do this is using the yx{\displaystyle {\sqrt[{x}]{y}}} feature on a scientific calculator. For example, to calculate 814{\displaystyle {\sqrt[{4}]{81}}}, you need to determine which number multiplied 4 times is equal to 81. Since 3×3×3×3=81{\displaystyle 3\times 3\times 3\times 3=81}, you know that 814=3{\displaystyle {\sqrt[{4}]{81}}=3}. So, the exponential expression now becomes 33{\displaystyle 3^{3}}. You should now have a whole number as an exponent, so calculating should be straightforward. You can always use a calculator if the numbers are too large. For example, 33=3×3×3=27{\displaystyle 3^{3}=3\times 3\times 3=27}. So, 810.75=27{\displaystyle 81^{0.75}=27}.
Question: What is a summary of what this article is about?
Convert the decimal to a fraction. Simplify the fraction, if possible. Rewrite the exponent as a multiplication expression. Rewrite the exponent as a power of a power. Rewrite the base as a radical expression. Calculate the radical expression. Calculate the remaining exponent.
Article: When coping with the stress and the problems of day-to-day life, it can be easy to lose track of what truly motivates you. Finding these things can be really helpful in overcoming the low points in life and moving forward.   There are a wide variety of things that can be your motivation! For example, it can be your work, your hobbies, or your relationships, or a combination of all of these things. Any of these things can bring you joy, a feeling of accomplishment, and the motivation to keep moving through life. Make a list or write an entry in your journal about what motivates you most in life. This could be a quick list or a more thorough exploration of drives and propels you in life. Writing out your motivations will allow you to revisit them when you are feeling down and can't remember why you need to move forward. Try reawakening your inner child. Find a new hobby or something to take your mind off things for a period of time everyday. Volunteering is a great way to cope with life because it can show you both the wonderful things in life and the way you can specifically can make a difference in the world. If there are things in life that bring you joy, find a way to work that into your volunteer work.  For example, work with animals at a local shelter if you love pets, help out at community events even just picking up trash in your neighborhood if you are interested in the environment. It can be hard to see the beauty of life when you are weighed down by the troubles of life. However, in order to cope with life, it's important to find beauty and joy in the world. This can help you to relax and rebuild your strength when times get hard. This could include the beauty of art, moments of kindness between children, or the wonders of nature, just to name a few things. Sometimes finding motivation and purpose requires you to change a variety of things in your life. For example, it may be that you need to change jobs or manage your time differently in order to find satisfaction with your life. Whatever it is that you need to change, change in general can be scary. It may take a lot of conviction and perseverance to make the changes you need to. However, keep in mind that the ultimate payoff for following through with changing you life is a happier and more fulfilling life.
Question: What is a summary of what this article is about?
Think about what motivates you in life. Make yourself useful. Find moments of joy and beauty. Make room for change.
Article: Unless you have recently buzzed your hair, your haircut is likely a little uneven. But you don't need to shave your hair to start growing it out. Try to get your hair trimmed every 6-8 weeks as it grows to keep your top and sides roughly the same length. If your haircut remains uneven, it will eventually become noticeably longer in the back than on top. The last thing you want while you're growing out your hair is a mullet. Frequent scalp massages can increase the blood circulation and encourage faster hair growth. Massage for 5 minutes every day, applying firm pressure to your head. Dip your hands in coconut oil before massaging to introduce growth-promoting vitamins and minerals to your hair. " While growing out your hair, you will eventually get to a place where your 'do is neither long nor short. Don't give up and crop your hair short during this phase. Wear a hat or slick your hair back until it's even to get through the awkward stages. Don't throw away your clippers or say goodbye to your stylist the day you decide to grow your hair out. To combat unruliness as you grow your hair out, you'll need periodic haircuts. If your hair starts to look uneven and heading towards mullet territory, get a trim.  Let your hairstylist know that you're growing out your hair so she can give you an accommodating cut. Even after you reach your ideal length, aim for a trim every 6 to 8 weeks to avoid split ends.
Question: What is a summary of what this article is about?
Start out with an even cut, if possible. Massage your scalp daily to encourage hair growth. Have patience during your hair's "awkward phase. Adjust your cut periodically as your hair grows.