If Euler Totient function fails other methods to find the remainder for the modular exponentiation

Question

Modular exponentiation using Euler Totient Function for the below question. $$ 128 ^{343} \mod 527 $$ using totient function. Is there any other method to find the remainder of the question if totient function fails? Please provide me some valuable answer in Euler totient function or give the other methods to learn

Answer 1

$$128=2^7$$

$$\implies128^{343}=(2^7)^{343}=2^{2401}$$

Now using Carmichael Function, $$\lambda(527)=240$$

$\implies2^{2401}\equiv2^{2401\pmod{240}}\equiv2^1\pmod{527}$