25^-1/2 = 1/√25 = 1/5
My question is, why does 25^-1/2 turn into 1/√25 ???
Where did the negative exponent 1/2 of 25 go??!!
2006-09-27 13:13:59 · 10 answers · asked by J.Welkin 1 in Science & Mathematics ➔ Mathematics
The only math convention used here is that an exponent of 1/2 is represented by a square root sign. The negative exponent is not just a convention, its a mathmatical reality. Let me explain.
Begin by looking at 5^3, we know that it is 5*5*5. Next, multiply a couple of these together: 5^3 * 5^2 = (5*5*5) * (5^5) = 5^5. It's easy to show from this that exponents just add up. Similarly, look at (5^4)/(5^2) = (5*5*5*5)/(5*5) = 5^2. Do a couple of these and you will see that when you divide, exponents subtract. Extending the idea of adding exponents when multiplying to negative exponents gives: (5^4) * (5^-2) = 5^(4-2) = (5^4)/(5^2) = 5*5. So multiplying by a number with a negative exponent is the same as dividing by that number with a positive one, just like subtrating a negative number is the same as adding a positive. So:
25^(-1/2) = 1/(25^(1/2)) = 1/√25 = 1/5.
By the way, how do you type that cool square root sign?? I had to cut and paste it from your question.
2006-09-27 13:30:36 · answer #1 · answered by Pretzels 5 · 0⤊ 0⤋
any fractional exponent is a root.
Thus ^1/2 = squareroot, ^1/3 = cubic root, etc...
Any negative exponent is equal to the number's reciprocal.
Thus 2^-1 = 1/2, 10^-2 = 1/10^2 = 1/100, etc...
So, 25^-1/2 = 1/(25^1/2) = 1/[sqrt(25)] = 1/5
2006-09-27 20:20:12 · answer #2 · answered by ohmneo 3 · 0⤊ 0⤋
the negative exponent inverts the 25 to 1/25
the exponent 1/2 is the same as the square root therefore...
25^-1/2 = 1/ sq root 25
2006-09-27 20:20:45 · answer #3 · answered by The Cheminator 5 · 0⤊ 0⤋
I could well be wrong, but I always thought that this was a convention, not a derivation. In other words, we just agreed that a negative exponent meant put the thing in the denominator, not that there is some proof of why that means that. But it could be I just never came across such a proof or reason, which would be a real answer to your question.
2006-09-27 20:17:42 · answer #4 · answered by All hat 7 · 0⤊ 0⤋
This is the definition of a negative exponent, as follows:
x^(-a) = 1/(x^a)
2006-09-27 20:16:58 · answer #5 · answered by rscanner 6 · 0⤊ 0⤋
when ther is a number raised to an index that is a fraction. the denominator of that fraction may be replaced witha root sign and the numerator stii applies to the number itself
example: 8^2/3
=( i cant find the sign) the cube root of 8^2
=2^2
=4
2006-09-27 20:19:23 · answer #6 · answered by acinorev 1 · 0⤊ 0⤋
a negative exponent (raising something to a negative power) is the same thing as taking its root...
so raising a number to "-1/3", for instance, is the same as taking its cubed root...
2006-09-27 20:18:09 · answer #7 · answered by Anonymous · 0⤊ 0⤋
I have no idea. to early to have a math headache. Hope someone else can help you.
2006-09-27 20:16:18 · answer #8 · answered by Totoru 5 · 0⤊ 0⤋
DO Your OWN MATH homework.
2006-09-27 20:16:37 · answer #9 · answered by Mike R 5 · 0⤊ 0⤋
SIMPLE YOU CALL THAT SIMPLE
2006-09-27 20:16:16 · answer #10 · answered by Anonymous · 0⤊ 0⤋