已知2的X次方*3的Y次方*5的Z次方=10800,XYZ为正整数,求(X+Z-5)的-Y次方_数学解答

已知2的X次方*3的Y次方*5的Z次方=10800,XYZ为正整数,求(X+Z-5)的-Y次方

人气：154 ℃　时间：2019-10-10 03:34:57

解答

10800=108*100 = 4 * 27 * 4 * 25 = 16 * 27 * 25 = 2^4 * 3^3 * 5^2
2^X * 3^Y * 5^Z = 10800,XYZ为正整数
X=4,Y=3,Z=2
(X+Z-5)^(-Y) = (4+2-5)^(-3) = 1^(-3) = 1