Given 1 / M + 1 / N = 1 / 6 1 / N + 1 / P = 1 / 9 1 / P + 1 / M = 1 / 15, we can find the value of MNP / Mn + NP + PM

Given 1 / M + 1 / N = 1 / 6 1 / N + 1 / P = 1 / 9 1 / P + 1 / M = 1 / 15, we can find the value of MNP / Mn + NP + PM

According to the conditions, it is necessary to add up all the three formulas
2(1/m+1/n+1/p)=1/6+1/9+1/15=15/90+10/90+6/90=31/90
therefore
1/m+1/n+1/p=31/180
thus
mnp/mn+np+pm=1/(1/m+1/n+1/p)=180/31

Calculation: (x / y ^ 3) ^ - 2 calculation: M + n / M-N divided by Mn + m ^ 2 / 2m
Note: detailed steps should be taken!

（x/y^3）^-2 =x^(-2)/y^(-6)=y^6/x^2
Calculation: M + n / M-N divided by Mn + m ^ 2 / 2m
=(m+n)/(m-n)*2m/m(m+n)
=2/(m-n)

The result of calculating the third power of (m power n) × (- M fourth power n) divided by (- Mn) is
No Baidu

^That is, (m ^ 2n) ^ 3 × (- m ^ 4N) / (- Mn) ^ 2 = (m ^ 6N ^ 3) × (- m ^ 4N) / (m ^ 2n ^ 2) = - m ^ (6 + 4-2) n ^ (3 + 1-2) = - m ^ 8N ^ 2, which is the second power of negative M's eighth power n. if you agree with my answer, please click "adopt as satisfactory answer" in the lower left corner