Question

whats the unit digit of 2^40*3^6

Answer 1

u mean 4?

Answer 2

take mod 10

Answer 3

its coming 4

Answer 4

units digit = \(\large 2^{40}*3^6 \mod 10\)

Answer 5

yes

Answer 6

3(9)*8^(13)*2

Answer 7

2^40 should be in 10s form

Answer 8

lets work it step by step

Answer 9

units digit = \(\large 2^{40}*3^6 \mod 10\)

\(\large \equiv 2^{40}*9^3 \mod 10\)

Answer 10

\(\large \equiv 2^{40}*(-1)^3 \mod 10\)

Answer 11

\(\large \equiv - 2^{40} \mod 10\)

Answer 12

fine, so far ?

Answer 13

yess

Answer 14

\(\large \equiv - 2^{5\times 8} \mod 10\)

Answer 15

\(\large \equiv - (32)^{8} \mod 10\)

Answer 16

\(\large \equiv - (2)^{8} \mod 10\)

Answer 17

still fine ?

Answer 18

yes

Answer 19

\(\large \equiv - (2)^{5+3} \mod 10\)

Answer 20

\(\large \equiv - (2^5)(2^3) \mod 10\)

Answer 21

\(\large \equiv - (32)(8) \mod 10\)

Answer 22

\(\large \equiv - (2)(8) \mod 10\)

Answer 23

-2*-2

Answer 24

Yep !

Answer 25

ye got it

Answer 26

\(\large \equiv -(2)(8)\mod 10\)

\(\large \equiv -(2)(-2)\mod 10\)

\(\large \equiv 4 \mod 10\)