Question

What is the unit place digit in 35(55)+35(36)

Answer 1

Answer:

36234 since 6 is unit digit and any power to 6 will be 6

⇒  33512 here 3 is unit digit so take last two terms of power i.e 12 and divide by 4 (because 3 has cyclicity of 3,9,7,1). So 12/4 i.e reminder 0 so unit digit will be 1.

⇒   39180 here 9 is unit digit same process repeat as above did. 80/2 (here divide by 2 because 9 has only 2 cycle 9 & 1 rem 0 ) so unit digit 1.

⇒  5429 - unit digit 4.

⇒  25123 - any power to 5 will be 5.

⇒  31512 - any power to 1 will be 1.

⇒  So, (6×1×1)−(4×5×1)=06−20

⇒  Subtract unit digit = 6−0=6

∴   The unit digit in given expression will be 6.

Step-by-step explanation:

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Answer 2

Answer:

$35 \times 55 + 35 \times 36$

$1925+ 1260$

$3185$

so the unit place is 5