what is the digit in the ones place of the solution to 3^63
To find the digit in the ones place of the solution to 3^63, we can use the concept of modular arithmetic.
First, let's find the pattern in the ones digit of powers of 3. We will calculate several powers of 3:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
From the pattern, we observe that the ones digit repeats in cycles of four: 3, 9, 7, 1.
Now, the exponent 63 is divisible by 4 (63 รท 4 = 15 remainder 3). Hence, we can determine that 3^63 has the same ones digit as 3^3, since they fall in the same position within the cycle.
Calculating 3^3 = 27, we find that the digit in the ones place of the solution to 3^63 is 7.