5. Power cyphers using the product of two large primes were first introduced by Rivest, Shamir, and Adleman in 1978. In modern enciphering terminology the power used to encipher is called the public key, and the power used to decipher is called the private key. Given that we are working in \(\mod 11009\) and using a public key of 77 find the private key. (Note: \(11009=101\cdot 109\))