How many IPv6 IP addresses are there?

IPv6 uses a 128-bit address which allows for 2¹²⁸ , or approximately 3.4 x 10³⁸ addresses. 3.4 x 10³⁸ is equal to 340 undecillion IP addresses. 
 
Therefore, there are 340,000,000,000,000,000,000,000,000,000,000,000,000 IPv6 addresses.