#Radiciation #Squareroot #SquareRoot Property #SquareRootomPotency #Squareroot Exponent
Continuing the properties of rooting, we can have the root of a root. So we have the root "n", from the root "p" of "a". Normally speaking is very bad, we normally calculate the exercise without reading it, but here we are going to read it.
Again we know that all radiciation is a divided exponent. So we have "a" to the 1 over "p", everything to the 1 over "n", remember we've multiplied the exponents, and so we have "a" to the 1 divided by "p" times "n", which is the root "p" times "n" of "a".
In any practical use of radiciation, the square root drawing is not used, but divided exponents. So it's good to understand the foundation.
Now let's do the exercise in practice.
So we have root 14 of the sixth root of 16. Again knowing that root is merely the exponential division, we have 16 to the 1 divided by 6, everything to the 1 divided by 14. Multiplying the exponents, we have 16 to the 1 divided by 6 times 1 divided by 14.
Remembering that 16 is 2 to the 4, that is 2 times 2, times 2, times 2, we have 2 to the fourth. So we multiply the exponent by 4, and doing this calculation we have the value of 1 divided by 21, which results in root 21 of the value 2.
Remember one thing, it may seem a little complicated, but it is necessary to learn it as quickly as possible, as such things will be foundational in other knowledge of Mathematics. Not learning can lead to getting lost in more complicated subjects.
sqrt[n]{sqrt[p]{a}}=left ( a^{frac{1}{p}}
ight )^{frac{1}{n}}=a^{ frac{1}{p}.frac{1}{n}}=a^{frac{1}{pn}}=sqrt[pn]{a}
sqrt[14]{sqrt[6]{16}}=left ( 16^{frac{1}{6}}
ight )^{frac{1}{14}}=16^{ frac{1}{6}.frac{1}{14}}=2^{frac{4}{1}.frac{1}{6.14}}=2^{frac{4}{1 }.frac{1}{6.14}}=2^{frac{1}{21}}=sqrt[21]{2}
