Examine a Simpler Case
ANSWER
Understand
You know that 3⁵⁰ is a large number to calculate. You need to find the number in the ones place.
Plan
It is not easy to simplify 3⁵⁰ with paper and pencil. Simplify easier expressions such as 3², 3³, and 3⁴, to see what number is in the ones place.
Carry Out
The table shows the values of the first 10 powers of 3.
You know that 3⁵⁰ is a large number to calculate. You need to find the number in the ones place.
Plan
It is not easy to simplify 3⁵⁰ with paper and pencil. Simplify easier expressions such as 3², 3³, and 3⁴, to see what number is in the ones place.
Carry Out
The table shows the values of the first 10 powers of 3.
Notice that the ones digit in the value column repeat in the pattern 3, 9, 7, and 1. Every fourth power of 3 has a ones digit of 1. Since 4 is divisible by 4, 3⁴⁸ has a ones digit of 1. Then the ones digit of 3⁴⁹ is 3 and the ones digit of 3⁵⁰ is 9.
Check
When the exponent of 3 is 2, 6, or 10, the ones digit is 9. The numbers, 2, 6, and 10 are divisible by 2 but not by 4. Since 50 is divisible by 2 by not 4, the ones digit of 3⁵⁰ is 9.
When the exponent of 3 is 2, 6, or 10, the ones digit is 9. The numbers, 2, 6, and 10 are divisible by 2 but not by 4. Since 50 is divisible by 2 by not 4, the ones digit of 3⁵⁰ is 9.