Question

What is the unit digit in the product (3)^{166} + (5)^{159}?

Answer 1

Answer:

5469

Step-by-step explanation:

3^2 * 166 + 5^2 * 159

9 * 166 + 25 * 159

= 5469

Answer 2

• Any number to the power 5 will have its unit digit as 5.
• Observing the powers of 3, we see :3¹=3(3ⁿ⁺¹)

                                                                   3²=9(3ⁿ⁺²)

                                                                   3³=27(3ⁿ⁺³)

                                                                   3⁴=81(3ⁿ⁺⁴)

                                                                   3⁵=243 (3ⁿ⁺¹)

• The unit place of powers of 3 repeat after every 4 numbers.
• 166 divided by 4 gives remainder as 2 so it is of form 3²=9(3ⁿ⁺²), ∴ unit place will be 9.
• 3¹⁶⁶(unit place)=9 and 5¹⁵⁹(unit place)=5.
• 9+5=14, unit digit =4.
• ∴Unit digit of the product=4