每日一题

Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

What is the largest possible integer value of n for which 5^n divides 50^7?

(A) 2
(B) 7
(C) 9
(D) 10
(E) 14

答案和解析

答案：E

解析：

Choice (E) is correct. Since 50 = 2*5^2, it follows that 50^7= (2*5^2)^7. Applying the laws of exponents to the preceding equality yields 50^7 = (2^7)*(5^14). From this representation of 50^7, it follows that 5^14divides 50^7 and that 14 is the largest value of n for which 5^n divides 50^7.