/sci/ - Science & Math » Thread #11225874

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Anonymous Sat 14 Dec 19:40:44 2019 No.11225874 View Reply Original Report

Quoted By: >>11225880 >>11225989 >>11225999

Hi /sci/, I'm having a bit of a brainlet moment, me and a friend are arguing over elevating whole numbers with numbers with decimal points in them (neither of us finished high school).
For example 4^0.5 and 4^0.25, what is the 4 being multiplied by? My friend says it's 4 x 4 x0.25 in the second case but that doesn't make sense to me since that gives 1 and in the calculator 4^0.25 gives 1.14etc, pls answer and no bully, thx

Anonymous

Anonymous Sat 14 Dec 2019 19:44:03 No.11225880 Report

Quoted By: >>11225920

>>11225874
It's a root. 4^0.25=4^(1/4)=4?(4)

Anonymous

Anonymous Sat 14 Dec 2019 20:02:56 No.11225920 Report

Quoted By: >>11225967

>>11225880
Sorry, I still don't understand how:
4^0.25 = 1.41421356237
and
4^0.25 = 1
can u explain pls, thx

Anonymous

Anonymous Sat 14 Dec 2019 20:29:00 No.11225967 Report

Quoted By:

>>11225920
4^0.25 does not equal 1.
4^0.25 = 4^(1/4), the fourth root of 4. Since it's the fourth root of 4, multiplying 4^(0.25) by itself four times gives 4.
Similarly, 4^(0.2) = 4^(1/5), the fifth root of 4, so multiplying 4^(1/5) by itself five times gives 4.
In general, if you have x^(m/n), where m and n are integers, (n a positive integer), x^(m/n) is the nth root of x^m, or in other words a number which, when multiplied by itself n times, give x^m. Equivalently, x^(m/n) is the mth power of the nth root of x, or in other words what you get when you multiply the nth root of x by itself m times.
An important fact of exponents is that x^(a*b) = (x^a)^b = (x^b)^a, which is why the two explanations of x^(m/n) are the same.

Anonymous

Anonymous Sat 14 Dec 2019 20:36:46 No.11225989 Report

Quoted By:

>>11225874
its the square root of some number to the power of another number

the square root of two is 2^1/2
the cubed root of two is 2^1/3

then... 2^2/3 is just (2^1/3)^2

in math, when you raise some number by another exponent, you multiply those exponents

(2^1/3)^2=(2^(1/3)*2)=2^(2/3)

Anonymous

Anonymous Sat 14 Dec 2019 20:42:35 No.11225999 Report

Quoted By:

>>11225874
.25 = 1/4
4^.25 = 4^(1/4). This is the fourth root of four. In other words, what number times itself 4 times will get you for. Another example 8^(1/3) = 2 because 2*2*2 = 8. In general any number, (barring imaginary numbers) x to the power of 1/n x^(1/n) means what number multiplied by itself n times will give you x.

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