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Mademuasel [1]
3 years ago
12

What is the units digit of 2 to the 50th power

Mathematics
1 answer:
11111nata11111 [884]3 years ago
6 0
Notice that

2^1=2
2^2=4
2^3=8
2^4=16
2^5=32

so that for each power of 2, there is a pattern of period 4. This means that for integers k\ge0, each of 2^{4k}, 2^{4k+1}, 2^{4k+2}, and 2^{4k+3} have the same units digit.

We can write 50=4(12)+2, and since 3=4(0)+2, it follows that 2^{50} and 2^3 share the same units digits. So the units digit of 2^{54} is 8.
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