# Back To Basics II

Algebra Level 5

$x,y,$ and $z$ are real numbers satisfying the equation $x^{2}+y^{2}+z^{2}=1.$

The maximum value of $3xy^{2}z$ can be expressed in the form $\dfrac{a}{b}$ for co-prime positive integers $a$ and $b$.

Find $a+b$.

Bonus:

Can you generalize the maximum value of $x^{m}y^{n}z^{p}$ for positive integers $m,n,p$ given the same constraints?

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