Prove the divisibility of the following numbers:

Question

45^45·15^15 by 75^30

Answer 1

45 = 5 * 9 = 5* 3 * 3
15 = 5 * 3
75 = 5 * 5 * 3
so
top = 5^45 * 3^90 * 5^15 * 3^15 = 5^60 * 3^105
bottom = 5^60 * 3^30
well, 3/3 = 1 :)

Answer 2

45^45·15^15 by 75^30

45^45·15^15 / 75^30
= (15)^45*3^45*15^15 / (15^30*5^30)
= 15^15*3^45*3^15*5^15 / 5^30
= 3^15*5^15*3^45*3^15*5^15 / 5^30
= 3^75 * 5^30 / 5^30
= 3^75

yup!

Answer 3

thank you both