By my interpretation, you should be OK, but don't take my word for it.
If the pistol is unloaded, cased, and cased again in a backpack, I would think that it would not be considered "readily accessible".
Is there a reason you want to carry it cased in a backpack, as opposed to another method?
76-10-523. Persons exempt from weapons laws.
(1) This part and Title 53, Chapter 5, Part 7, Concealed Weapon Act, do not apply to any of the following:
(a) a United States marshal;
(b) a federal official required to carry a firearm;
(c) a peace officer of this or any other jurisdiction;
(d) a law enforcement official as defined and qualified under Section 53-5-711;
(e) a judge as defined and qualified under Section 53-5-711;
(f) a common carrier while engaged in the regular and ordinary transport of firearms as merchandise; or
(g) a nonresident traveling in or through the state, provided that any firearm is:
(i) unloaded; and
(ii) securely encased as defined in Section 76-10-501.
(2) The provisions of Subsections 76-10-504(1) and (2), and Section 76-10-505 do not apply to any person to whom a permit to carry a concealed firearm has been issued:
(a) pursuant to Section 53-5-704; or
(b) by another state or county.
As used in this part:
(18) "Securely encased" means not readily accessible for immediate use, such as held in a gun rack, or in a closed case or container, whether or not locked, or in a trunk or other storage area of a motor vehicle, not including a glove box or console box. <--- This green part does not apply if the vehicle is in your lawful possession,see below.
76-10-504. Carrying concealed dangerous weapon -- Penalties.
(1) Except as provided in Section 76-10-503 and in Subsections (2), (3), and (4), a person who carries a concealed dangerous weapon, as defined in Section 76-10-501, including an unloaded firearm on his or her person or one that is readily accessible for immediate use which is not securely encased, as defined in this part, in or on a place other than the person's residence, property, a vehicle in the person's lawful possession, or a vehicle, with the consent of the individual who is lawfully in possession of the vehicle, or business under the person's control is guilty of a class B misdemeanor.
(2) A person who carries a concealed dangerous weapon which is a loaded firearm in violation of Subsection (1) is guilty of a class A misdemeanor.
(3) A person who carries concealed a sawed-off shotgun or a sawed-off rifle is guilty of a second degree felony.
(4) If the concealed firearm is used in the commission of a violent felony as defined in Section 76-3-203.5, and the person is a party to the offense, the person is guilty of a second degree felony.
(5) Nothing in Subsection (1) or (2) shall prohibit a person engaged in the lawful taking of protected or unprotected wildlife as defined in Title 23, Wildlife Resources Code of Utah, from carrying a concealed weapon or a concealed firearm with a barrel length of four inches or greater as long as the taking of wildlife does not occur:
(a) within the limits of a municipality in violation of that municipality's ordinances; or
(b) upon the highways of the state as defined in Section 41-6a-102.