MathRevolution wrote:
What is the units digit of \(248^{20}\)?
A. 0
B. 2
C. 4
D. 6
E. 8
Look for a
pattern248^1 = 24
8248^2 = (248)(248) = ---
4 [aside: we need not determine the other digits. All we care about is the units digit]
248^3 = (248)(248^2) = (248)(---4) = ----
2248^4 = (248)(248^3) = (248)(---2) = ----
6248^5 = (248)(248^4) = (248)(---6) = ----
8NOTICE that we're back to where we started.
248^5 has units digit
8, and 248^1 has units digit
8So, at this point, our pattern of units digits keep repeating
8, 4, 2, 6, 8, 4, 2, 6, 8,...We say that we have a "cycle" of 4, which means the digits repeat every 4 powers.
So, we get:
248^1 = --
8248^2 = ---
4 248^3 = ----
2248^4 = ----
6248^5 = ----
8248^6 = ---
4 248^7 = ----
2248^8 = ----
6248^9 = ----
8248^10 = ----
4 etc.
Notice that when the exponent is a MULTIPLE of 4 (4, 8, 12, 16, ...), the units digit will be
6Since 20 is a MULTIPLE of 4, we know that the units digit of 248^20 will be
6Answer:
Here's an article I wrote on this topic (with additional practice questions):
https://www.gmatprepnow.com/articles/un ... big-powers Cheers,
Brent
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