2006-06-10 03:58:37 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Rational exponents are exponents that are rational numbers.
That is numbers that can be expressed as a fraction with whole number numerators and denominators.
When a number raised to the 1/n power, it is the same as taking the nth root of that number. When a number is raised to the m/n power it is the same as taking the nth root and raising it to the mth power (or taking the mth power and then taking the nth root of that).
A radical is the symbol that incicates that a root is being taken.
2006-06-10 04:06:36 · answer #1 · answered by rt11guru 6 · 1⤊ 1⤋
First of all, I like the two previous answers, and would like to just add something:
There is one thing (at least) that you need to be very aware of when dealing with rational exponents in the real numbers. All rational numbers n/m can be written in a reduced form p/q where n/m=p/q and p and q are "relatively prime" (that means no prime can divide both p and q, thus no number not equal to 1 can divide both p and q). Insbesodere p and q are not both even (because if they were both even, then 2 would divide both).
If you have a^(n/m)=a^(p/q) for some a<0 you can have problems. If q is odd than you won't have a problem at all, but if q is even, you won't get a real answer.
This is why (assume q is even and a<0):
q is even, so q=2s for some s. Thus a^(p/q)=a^(1/2)(1/s), but since a<0, a^(1/2) (which equals sqrt of a, of course) is complex and not real, so a^(p/q) is complex and not real.
2006-06-10 05:09:43 · answer #2 · answered by Eulercrosser 4 · 0⤊ 0⤋
The use of rational numbers as exponents. A rational exponent represents both an integer exponent and an nth root. The root is found in the denominator (like a tree, the root is at the bottom), and the integer exponent is found in the numerator.
Radical is derived from the Latin word radix, which means "root". In mathematics, the radical symbol (square root symbol) used to indicate the nth root of a number.
2006-06-10 04:10:56 · answer #3 · answered by organicchem 5 · 0⤊ 0⤋
adding to eulercrosser dude, radicals also mean that the answer is positive. i.e. 16^(1/4) = +or- 2 while 4th root of 16 represented as a radicle = +2 only.
2006-06-10 09:33:05 · answer #4 · answered by Morkeleb 3 · 0⤊ 0⤋
racials are square roots.
2006-06-10 04:00:47 · answer #5 · answered by joey 2 · 0⤊ 0⤋