# Remainder=?

##### 2 Answers

This can be calculated in a number of ways. One way using brute force is

#27^1/7# has a remainder#=6# .....(1)

#27^2/7=729/7# has a remainder#=1# .....(2)

#27^3/7=19683/7# has a remainder#=6# …….. (3)

#27^4/7=531441/7# has a remainder#=1# ….. (4)

#27^5/7=14348907/7# has a remainder#=6# …..(5)

#27^6/7=387420489/7# has remainder#=1# …. (6)

As as per emerging pattern we observe that the remainder is

Given exponent is

Alternate solution

#### Explanation:

Given number needs to be divided by

#(27)^999#

#=>(28-1)^999#

In the expansion of this series, all terms which have various powers of

We see that this term

Since remainder can not be

This will leave remainder as