Exponents in the Real World?
921370
You have packing boxes that are 2 feet on a side.  You will be stacking them two high, two wide, two deep.  How many total cubic feet can you put in the boxes?\n\n2^3 * 2^3 = 2^6 = 64 cu. ft.
163546
Exponential graphs appear EVERYWHERE in the real world. \n\nFor example, they are used in :\n\n1. radioactive dating\n2. acoustic analysis of theatres\n3. stock market management\n4. estimation of stellar magnitudes\n5. analysis of the pH of solutions\n6. analysis of earthquakes\n7. tuning pianos\n8. tempering musical scales\n\nand many many more places.
316406
Depends on how fast you're counting...\n\nhttp://hub1.worlded.org/docs/maththing/ny1p5.htm\nhttp://mathforum.org/library/drmath/view/58739.html
240636
The degree is the highest exponent on the variable.\nThe exponent of x is one.\nThus, the degree of 4x is 1.
819914
Remember - a negative exponent is an inverse.  If all you are doing is multiplying and dividing, life is easy.\n\n(3a^-7 b^7)/(9a^7 b^-5)\n\nFirst, move the negatives from where they are to the other side of the miniscis:\n\n= (3 b^7 b^5)/(9 a^7 a^7)\n\n(You can verify this by rewriting, for instance, a^-7 as 1/a^7 and simplifying, but I promise you this works.)\n\nNow:  3/9 = 1/3\n\nb^7 b^5 = b^12\n\na^7 a^7 = a^14\n\nSo, b^12/(3 a^14) and we're done.\n\nIf there were addition and subtraction in the problem, then it gets an order of magnitude harder.  Then, there is no substitute for rewriting the negative exponents as reciprocals and simplifying from there.\n\nHope this helps.
751243
One property of exponents is \n\na^m * a^n = a^(m+n)\n\nSo x^-5/6 * x^-4 * x^-2 =\n=x^(-6+-5/6) \n=x^-41/6\n=sixth root of 1/x^41
888996
http://en.wikipedia.org/wiki/Indefinite_and_fictitious_large_numbers\n\nlook at that
258044
divide the exponent by two
192782
It's not in scientific notation. The number you are multiplying by 10^x has to be between 1 and 10 for the equation to be scientific notation. You just made an algebraic expression. Isthe number you are trying to "notate" 80? It would just be 8 x 10^1, or 8 x 10.
720847
Use logarithms. If you haven't learned them yet, it just helps to solve equations with powers.\na = b^x\nlna = ln(b^x) = xlnb\nx = lna/lnb\nx = ln(10)/ln(32.6087)\nx = 0.6607928852\nYou can use your calculator to check. I guarentee that it works.
663667
It is true when both exponent & base are the same.\n\nOtherwise, they have to satisfy the formula:\n\na = r^(1/(r-1))\nb = r^(r/(r-1))\n\nwhere you can plug in any value for 'r' & get a, b - these are the two numbers we want.\n\n\nExamples:\n\n1. Suppose r=2,\n\na = 2^(1/(2-1)) = 2^1 = 2\nb = 2^(2/(2-1)) = 2^2 = 4\n\nAs you have shown yourself, 2^4 = 4^2.\n\n\n2. Suppose r=1.5,\n\na = 1.5^(1/(1.5-1)) = 1.5^2 = 2.25\nb = 1.5^(1.5/(1.5-1)) = 1.5^3 = 3.375\n\nYou can show using a calculator that 2.25^3.375 = 3.375^2.25\n\n\nP.S. Another very interesting property you will notice is that:\nb=(a*r) & b=(a^r)\n\nsimultaneously!
1187309
I think I did it.  If y=1/log(x), then a few manipulations gave me\n\nx=10^(1/y).\n\nI'm assuming by log you mean log to the base 10.  I suppose mathematicians will start fussing about what happens at y=0, but a physicist like me doesn't worry that much about infinities ...
788532
Is it x*(e-2) or x^(e-2)?\n\nI don't think it matters anyway, because the bottom fluctuates between 3 and 5 while the top increases indefinitely, i.e. approaches "infinity" if you like.  So there's no limit.
53602
You need to round off the number to 4 digits and use the proper exponent to reflect the entire number:\n\n1.496 x 10^11  Your first answer is correct.
731776
simple!!!\nthe answer is : 12x^2\nthe rule of addition intergers with exponents is simple.\nyou just add the whole number (that is 4+8) and then follow the integers (that is x^2)... get my point?\ni hope i have helped you with your assignment....
178588
Rearrange as (-7)(-11) m^(-6) m^(-4) u^(-4). Then combine the two coefficients into 77, and add exponents for the same base m, to get m^(-10). The final result is \n77 m^(-10) u^(-4). By the way, you should ask your teacher or consult the book to see if exponents should be made positive. In that case write the answer as 77 / [m^10 u^4].
64159
It's debatable.  Here's an interesting column that addresses the question:\nhttp://mathforum.org/library/drmath/view/57188.html