How to calculate Public Key exponent if I have p, q, Dp, Dq, QInv? I have a private key components p, q, Dp, Dq, and QInv. I need to calculate the public key modulus and exponent. Modulus was super simple p*q, but exponent I can't figure out. Have searched all the articles and often found how to go opposite way - generating public private key once you pick the exponenet.

I have been trying ModInverse from p-1 and q-1, and solve x with GCD on all the componenets, but nothing gave me the right value (I know the value I should get is x010001). Seems to be a little bit more complex that this...

Im really in to the code and less in math, so if I could get the answer which use simple math operations as 'Add', 'Sub', 'Multiply', 'Mod', 'ModInverse', 'GCD' etc. would be great!
Your public key contains two numbers. First it is a number n, which is called the Modulus and are computed through $p \cdot q = n$.
The second number is e, which is the public exponent and are used to encrypt your message m. The number e is choosen that it have the following properties:

\begin{equation}
1 &lt; e &lt; \phi(n) = (p-1)(q-1)
\end{equation}
\begin{equation}
gcd(e, (p-1)(q-1)) = 1 
\end{equation}

$\phi$ is the euler's totient function.

The private key contains the numbers p,q and d. The number d is your private exponent and p,q are your prime numbers, which helps you do calculate n and the private and public exponent. 

The private exponent have the following properties:

\begin{equation}
1 &lt; d &lt; (p-1)(q-1)
\end{equation}
\begin{equation}
d = e^{-1} mod~(p-1)(q-1)
\end{equation}

I am not sure, what are Dp, Dq and QInv in your configuration is, but if you have d you are able to compute e with:

\begin{equation}
e = d^{-1} mod~(p-1)(q-1)
\end{equation}

I hope it will help you. If that doesn't help may specifiy what are Dp, Dq and QInv are. 

EDIT:
I think you are using the PKCS#1, which are mentioned in the comments below of this answer.

In the PKCS#1 you are also able to have a quintuple as a private key, which are p, q, Dp, Dq and QInv.

Dp and Dq satisfy the following equations:

\begin{equation}
e \cdot Dp \equiv 1~mod~(p-1) \Leftrightarrow e = Dp^{-1} ~mod ~(p-1) \\
e \cdot Dq \equiv 1~mod~(q-1) \Leftrightarrow e = Dq^{-1} ~mod ~(q-1)
\end{equation}

and the number e have a little bit different property.
The property of e is:

\begin{equation}
gcd(e, \lambda(n)) = 1~and~\lambda(n) = LCM(p,q)
\end{equation}

Additionally your d is satisfying this equation instead of that from above:

\begin{equation}
ed \equiv 1 ~mod ~\lambda(n) \Leftrightarrow e = d^{-1} ~mod ~\lambda(n) 
\end{equation}

This equation should give you the right e from your giving d and $e = d^{-1}~mod~\lambda(n)$ means compute the modular inverse from d with the modulus $LCM(p,q)$.

I hope this will help you.