Asked by Helen
Prove the divisibility of the following numbers:
45^45·15^15 by 75^30
45^45·15^15 by 75^30
Answers
Answered by
Damon
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 :)
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 :)
Answered by
Reiny
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!
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!
Answered by
Helen
thank you both
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