Question

What is the unit digit in 32 power 46+58 power 72?​

Answer 1

Answer:

0

Step-by-step explanation:

32 power 46

unit digit, so take only 2----> 2^46

Cyclicity of 2 is 4

46/4, Rem=2

Thus, units digit= 4

58 power 72

= 8 power 72

= 2 power 216

Again cyclicity of 2 is 4

216/4, Rem=0

Thus, units digit= 6

Final units digit= 4+6 = 0

Hope you understood!

Answer 2

Answer:

unit digit is 0.

${32}^{46} + {58}^{72}$

${32}^{46} = {(30 + 2)}^{46}$

only term in this expansion that will not have 0 as unit digit will be 46C46x2^46

which will have unit digit of 2^46

=4

similarly for

${58}^{72} = {(60 - 2)}^{72}$

only term in this expansion that will not have 0 as unit digit will be 72C72 x 2^72

which will have unit digit of 2^72

=6

so adding 4+6=10

hence we will have 0 as unit digit.