Question

Find the units digit for the sum 13^25 + 4^81 + 5^411?​

Answer 1

Answer:

So 5^411 has unit digit 5. Units digit of 3^25+4^81+5^411 = 3+4+5=12 or Units digit is 2. Answer. Alternatively use power cycles of 3,4 and 5 to get unit digit.

Step-by-step explanation:

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Answer 2

The unit digit for the sum 13^25 + 4^81 + 5^411 is 2.

concept : Unit digit of every number repeats itself after every 4th power.

for example, let's take 12,

12¹ = 12⇒ unit digit = 2

12² = 144⇒unit digit = 4

12³ = 1728 ⇒unit digit = 8

12⁴ = 20736 ⇒unit digit = 6

12⁵ = 248832 ⇒unit digit = 2

you see, after every 4th power, unit digit of 12 repeats itself.

To find unit digit of any number of random power.

• at first divide the power of number by 4.
• after dividing, you will get remainder.
• now use the remainder as power of number.

number is ..

$13^{25}+4^{81}+5^{411}$

find unit digit of each term.

$13^{25}=13^{6\times4+1}=13^1$

hence, unit digit of 13²⁵ = unit digit of 13¹ = 3

similarly,

$4^{81}=4^{4\times20+1}=4^1$

hence, unit digit of 4^81 = unit digit of 4¹ = 4

for 5⁴¹¹, unit digit always will be 5. so no need to find out.

now unit digit of number = unit digit of (3 + 4 + 5) = 2

Therefore unit digit for the sum is 2.