Math CentralQuandaries & Queries


Question from 7th, a student:

Hello I am a 7th grader in the US and need some help.
I was doing my homework and had gotten stuck on one question. my friends told me to go to this website because it helps many students.
the question is: What is the unit digit of 47 to the 43rd power? Please answer as soon as possible. Thank you.

Hi there.

First, think about the 4 in 47. Because it is in the tens place, is there any way it can affect what happens in the units place? The answer is no, so you can be confident that the units digit of 4743 is the same as the units digit of 743.

Now look for a pattern. Anything that shows up in the tens column is no longer relevant:
71= 7
72 = 7 x 7, which ends in 9.
73 = (something ending in 9) x 7 = something ending in 3.
74 = (something ending in 3) x 7 = ??
Complete this and keep doing it until you see a repeating pattern, then you can project what the 43rd line will say.

Stephen La Rocque.

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