I need to know how to descibe the similarities between radicals and rational exponent notation.?
483647
Here's how:  square root is the same as the 1/2 power.\n\nSqrt (9) = 9^(1/2) = 3\n\nCube root is same as 1/3 power.\n\nFourth root same as 1/4 power, etc.\n\nIf you have an exponent of 2/3, thet's the cube root squared.\nSo 8^(2/3) = (cube root of 8)^2 = 4
860580
just divide the inside by a perfect square (i.e. 4,9,16) and write it like this\n(this is the first problem you have)\nV(3X9) because 3X9=27\ntake the square root of the perfect square and move it to the outside\n3V3\nwhen you already have a number outside the radical, multiply it by the number you just simplified from the inside of the radical\n3V32\n3V(16X2)\n3X4V2\n12V2
843761
well assuming you just want to break it down...\n1: you put the -2 power on both the 4 and a^3.  then it'd be (4^-2)(a^3^-2).\n2: remember that when it's an exponent to an exponent you multiply the numbers together so it becomes (4^-2)(a^-6)\n3: a negative exponent means it is one over itself so it would be 1/(4^2)(a^6)\n4: just simply from there to make it 1/ (16a^6)\n\nhopefully that was what you were asking!!
865479
First of all is the radical in the numerator over just the 10 or over the entire 10y^3?\n\nThe only this you can factor out and cancel is a radical 2 on the top and bottom.  Other than that, you can't really simplify this problem.  Are you sure you wrote it down correctly?
460242
ur answer is [sqrt(3) - sqrt(7)].it can written as sqrt[x +/- 2*sqrt[y]] when x=a^2 + b^2 and y=a*b is equal to sqrt(a) +/- sqrt(b)
323323
This is the best I could come up with:\n\n(a)  (x^2-4)(x^4+4x^2+16)\n      (x-2)(x+2)(x^4+4x^2+16)\n\n(b)  (x^3-8)(x^3+8)\n     (x-2)(x^2+2x+4)(x+2)(x^2-2x+4)\n\n(c)  If you take out the factors that are the same, what's left should be equal hence:\n     x^4+4x^2+16=\n(x^2+2x+4)(x^2-2x+4)\n\n(d)  x^(a^2)+2ax^a+4a^2=\n(x^a+ax+2a)(x^a-ax+2a)
444064
So, for a) & b) the two things that you should notice are:\n1 - The exponents inside the second polynomial alternate, meaning that as the powers of the x variable decrease, the powers of the y variable increase, both by increments of one.\n2 - The answer will only contain the variables x and y raised to the same power, which is one more than the leading exponent on the x variable.  \n\nSince (x + y)(x^2 - xy + y^2) = x^3 + y^3\n and  (x + y)(x^4 - x^3y + x^2y^2 - xy^3 + y^4) = x^5 + y^5,\nthen for any given polynomial the pattern is written out...\n(x + y)(y^2n - x^(2n-1)y + x^(2n-2)y^2 + ... + x^2y^(2n-2) - xy^(2n-1) + y^2n = x^(2n+1) + y^(2n+1)
785120
http://www.freemathhelp.com/forum/viewforum.php?f=9\nhttp://www.purplemath.com/modules/
1100619
Rational exponents are something like x^(2/3)\n\nwhich can be rewritten with radical sign as something like\n ____ \n/ 2^3\n\n\nThere is really no advantage except that most high school math curriculums de-emphasized the rational exponents in favor of the radical sign.  Even the radical is de-emphasized since it is easier to use the calculator.  The reason for the de-emphasis is that most high school graduate would never need to see a radical or rational exponents, except know why some calculators have a square root button.  If a student needs it in higher education, then that is left up to the higher educators.
311264
Well. Do you know how to work rational expressions in general? The first link below is a useful general resource and has a section on rational expressions and polynomial long division; the second is specifically on rational expressions at college intro-level.\n\nI used to tutor math and I found that most people's difficulty with word problems was not the actual math, it was extracting the appropriate equations from the words. Once they had the equations, they could solve them (assuming they'd learned the basics). \n\nI'd find it pretty difficult to give you general guidelines on "how to solve word problems with rational expressions" but the main trick with word problems is to figure out a) what variables are involved, and assign each of them a letter (e.g., speed of first train is x, time it has been travelling is y, speed of second train is z...), b) sort out the relationship between them (e.g. x = 2z/5), and c) make sure you know what *exactly* is being asked. It is not at all uncommon for word problems to include extraneous information (colour of train, age of driver) to muddle the issue.\n\nYour best bet is almost certainly to go ask your teacher, professor, TA, tutor, study group, or classmate-who-understands-it for help. They will be better able to figure out where your problem is if they can watch you work through an actual example.
498269
2-root-3 is the same as 2 ^ 1/3 (^ is exponent sign)\n\n2 ^ 1/3 squared is (2 ^ 1/3) ^ 2 ... you multiply the exponents, so it equals\n\n2 ^ 2/3
102907
Let:\nx = any number not equal to 0.\nm = any number\nn = any number\n\nProperty of exponents:\n\nx^m/x^n = x^(m-n)\n\nTherefore:\n1/1 =2/2 =3/3 = x/x = x^n/x^n = x^(n-n) = x^0 = 1
346393
all are the same\n\n10*10^5=\n1*10^6=\n2*10^5.7=\n4*10^5.4=\n100*10^4\n\ndecibels use a logarithmic scale so you have to compare them as exponents
917618
Since you're dividing two monomials with the same base (x), you subtract the exponents so the answer is x^6. \n\nHope this helps ;-)
235721
(3x²)²(1/3y²)²=(9x^4)(1/9y^4)=(x^4)/(y^4)\n\nin many computer languages the "^" symbol is used for exponents.
759262
The rules for simplifying integer exponents are pretty simple:\n\nhttp://en.wikipedia.org/wiki/Exponentiation
992834
u r probably working on order of operations, this might help:\nPlease (parantheses)\nExcuse (exponents)\nMy  (multiplication)\nDear (division)\nAunt (addition)\nSally (subtraction)\n\n1. 7000 x 400000 = 2800000000\n2.  1/144 = x^2 so x = +/- 1/12\n3.  -3 +/- the square root of 2\n4.  5t^4 - 7t^3 + 6t -2\n5.  4x^4 - 16x^2 +16