Math

Question Find the last digit of 3333333^{333}.

Studdy Solution

STEP 1

Assumptions
1. We are asked to find the last digit of the power 3333333^{333}.
2. The last digit of a number raised to a power depends on the last digit of the base and the power to which it is raised.

STEP 2

Identify the pattern in the last digit of powers of 3.
The last digit of powers of 3 follows a pattern: 3, 9, 7, 1, and then it repeats. This is because:
31=33^1 = 3 32=93^2 = 9 33=273^3 = 27 34=813^4 = 81

STEP 3

Notice that the last digit of 343^4 is 1, which means every fourth power of 3 will end in 1.

STEP 4

Determine the remainder when the exponent 333 is divided by 4, since the pattern repeats every 4 powers.
333mod4333 \mod 4

STEP 5

Calculate the remainder.
333mod4=1333 \mod 4 = 1

STEP 6

Since the remainder is 1, the last digit of 3333333^{333} will be the same as the last digit of 313^1, which is 3.
The last digit of the power 3333333^{333} is 3.

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