Question

find the value of 370^1231 + 130^1230

Answer 1

I am in 6 grade. I don't now this

Answer 2

Answer:

Concept:

Power cycle concept,  

For example,

21=2     25=32

22=4     26=64

23=8     27 =128

24=16    28 =256

It can be noticed that the unit digit gets repeated for every 4th power of 2. Hence we can conclude that 2 has a power cycle of 2,4,8,16 with a base value or frequency of 4.

Solution:

$370^{ 1231 }+130^{ 1230 } =(37^{ 1231 }\times \quad 10^{ 1231 })+(13^{ 1230 }+10^{ 1230 })$

Now divide the power values using the respective Base values / Frequencies:

$\frac{1231}{4}$ = Remainder is 3              

$37^{1231}$  will have it’ s unit digit as 3     (from the power cycle of 37)

$\frac{1230}{4}$ = Remainder is 2

131230 will have it’ s last digit as 9          (from the power cycle of 13)

We know that 10 raised to the power of anything will always result in a number with ‘0’ as it’s unit digit.

Unit digit value of $370^{ 1231 }+130^{ 1230 }  = 3 + 9 = 12 ,$” where  2 is the unit digit”

Therefore, the Unit digit value of $370^{ 1231 }+130^{ 1230 } = 2$