Question

unit digit of 793^3361+432^531+944^77​

Answer 1

Step-by-step explanation:

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Answer 2

Given:

A number in exponential form 793^3361+432^531+944^77​.

To Find:

The units digit of the given expression.

Solution:

1. The given number is 793^3361+432^531+944^77​.

2. The number can be also written as,

=> (790+3)^3361+(430+2)^531+(940+4)^77,

=> Any number whose units digit is 0 has a value of 0 for any positive power of that number. For example, 100^7483 has a units digit of 0.

3. The units digit of 3^n is,

• 3 for 4n + 1 values,
• 9 for 4n + 2 values,
• 7 for 4n + 3 values,
• 1 for 4n values.

4. The units digit of 2^n is,

• 2 for 4n + 1 values,
• 4 for 4n + 2 values,
• 8 for 4n + 3 values,
• 6 for 4n values.

5. The units digit of 4^n is,

• 4 if the value of n is odd,
• 6 if the value of n is even.

6. 3361 can be written as 4(840) + 1, hence the units digit of 3^ 3361 is 3.

7. 531 can be written as 4(132) + 3, hence the units digit of 2^531 is 8.

8. 77 is an odd value, hence 4^77 has the units digit 4.

9. Hence, the units digit of the given expression is,

=> 3 + 8 + 4 = 15,

=> Units digit = 5.

Therefore, the units digit of the expression 793^3361+432^531+944^77​ is 5.