Question

已知(x^y)^m × (xy^(n) z)^3 × Y^(4)z^6=x^5 × y^8 × z^p，求m+n+p的值

Answer 1

题目应是 (x^2y)^m × (xy^(n) z)^3 × Y^(4)z^6=x^5 × y^8 × z^p
x^(2m)y^m × (x^3y^(3n) z^3) × Y^(4)z^6=x^5 × y^8 × z^p
x^(2m+3) y^(m+3n+4) z^9=x^5 × y^8 × z^p
2m+3=5 m+3n+4=8 p=9
m=1 n=1 p=9
m+n+p=11

Answer 2

(x^y)^m × (xy^(n) z)^3 × Y^(4)z^6=x^5 × y^8 × z^p
左式=(x^y)^m × (xy^(n) z)^3 × Y^(4)z^6
=x^m*y^m*x^3*y^(3n)*z^3*y^4*z^6
=x^(m+3)*y^(m+3n+4)*z^(3+6)
=x^(m+3)*y^(m+3n+4)*z^9
即x^(m+3)*y^(m+3n+4)*z^9=x^5 × y^8 × z^p
所以
m+3=5,m=5-3=2
m+3n+4=8,3n=8-4-m=4-2=2,n=2/3
p=9
故m+n+p=2+2/3+9=11（2/3）