Question

find the remainder when 7 raised to the power 21 + 7 raise to the power 22 + 7 raise to the power 33 + 7 raise to the power 24 is divided by 25

Answer 1

you did little mistake to write :
question is ---> find the remainder when 7²¹ + 7²² + 7²³ + 7²⁴ is divided by 25.

first we should rewrite (7²¹ + 7²² + 7²³ + 7²⁴)
7²¹ + 7²² + 7²³ + 7²⁴ = 7²¹ + 7²¹⁺¹ + 7²¹⁺² + 7²¹⁺³
= 7²¹.1 + 7²¹.7¹ + 7²¹.7² + 7²¹.7³
= 7²¹( 1 + 7 + 49 + 343 )
7²¹ × 400

Now, divided by 25 , what you get remainder ?
zero , right ?
actually 400 is divisible by 25 , that's why reminder will be zero.