Question

若3×9^m×27^m=3²¹，则m=　　　　　　．                                                 

Answer 1

　4　．                                                                                             

【考点】幂的乘方与积的乘方；同底数幂的乘法．                                         

【分析】根据幂的乘方和积的乘方的运算法则求解．                                      

【解答】解：3×9^m×27^m=3×3^2m×3^3m=3^5m+1，                                            

故5m+1=21，                                                                                    

解得：m=4．                                                                                     

故答案为：4．                                                                                   

【点评】本题考查了幂的乘方和积的乘方，解答本题的关键是掌握幂的乘方和积的乘方的运算法则．