#### Question

If x^4+x^3+x^2+x+1 = 0, then the value of x^{25} is

Question

If x^4+x^3+x^2+x+1 = 0, then the value of x^{25} is

Given

x^4+x^3+x^2+x+1 = 0

(1)

Multiply both sides with x to raise the power of leading term to 5

x^5+x^4+x^3+x^2+x= 0

(2)

Subtracting (1) from (2) gives

x^5-1 = 0

Then

x^5 = 1

Using power rule for exponent

x^{25} = (x^5)^5 = 1^5 = 1

Therefore

the value of x^{25} is 1