Solved on Jan 27, 2024

Find the last digit of $33^{333}$ .

STEP 1

Assumptions
1. We are asked to find the last digit of the power $33^{333}$ .
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:
$3^1 = 3$ $3^2 = 9$ $3^3 = 27$ $3^4 = 81$

STEP 3

Notice that the last digit of $3^4$ 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.
$333 \mod 4$

STEP 5

Calculate the remainder.
$333 \mod 4 = 1$

STEP 6

Since the remainder is 1, the last digit of $33^{333}$ will be the same as the last digit of $3^1$ , which is 3.
The last digit of the power $33^{333}$ is 3.

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Find the last digit of $33^{333}$ .

STEP 1

Assumptions
1. We are asked to find the last digit of the power $33^{333}$ .
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:
$3^1 = 3$ $3^2 = 9$ $3^3 = 27$ $3^4 = 81$

STEP 3

Notice that the last digit of $3^4$ 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.
$333 \mod 4$

STEP 5

Calculate the remainder.
$333 \mod 4 = 1$

STEP 6

Since the remainder is 1, the last digit of $33^{333}$ will be the same as the last digit of $3^1$ , which is 3.
The last digit of the power $33^{333}$ is 3.

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Find the last digit of 3333333^{333}33333.

STEP 1

Assumptions1. We are asked to find the last digit of the power 3333333^{333}33333.2. 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 = 331=3 32=93^2 = 932=9 33=273^3 = 2733=27 34=813^4 = 8134=81

STEP 3

Notice that the last digit of 343^434 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.333mod 4333 \mod 4333mod4

STEP 5

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

STEP 6

Since the remainder is 1, the last digit of 3333333^{333}33333 will be the same as the last digit of 313^131, which is 3.The last digit of the power 3333333^{333}33333 is 3.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the last digit of $33^{333}$ .

Assumptions
1. We are asked to find the last digit of the power $33^{333}$ .
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.

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:
$3^1 = 3$ $3^2 = 9$ $3^3 = 27$ $3^4 = 81$

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

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

Calculate the remainder.
$333 \mod 4 = 1$

Since the remainder is 1, the last digit of $33^{333}$ will be the same as the last digit of $3^1$ , which is 3.
The last digit of the power $33^{333}$ is 3.