Bitcoin don't use RSA but ECDSA.
Your private key D is a 256bits unsigned integer.
Then, you can calculate your public key by multiplying D with a generator point G on an elliptic curve.
On bitcoin, the standard is https://en.bitcoin.it/wiki/Secp256k1.
There is no exponent, or i don't understand what you call exponent (since it's not RSA).