The cell organelle that serves as the carrier of power synthesized by mitochondria is the Adenosine Triphosphate (ATP). ATP is often referred to as the "molecular currency" of the cell as it provides the necessary energy for various cellular processes.

Mitochondria and ATP Production:
1. Mitochondria are the powerhouses of the cell and play a crucial role in cellular respiration.
2. Cellular respiration is the process by which cells convert nutrients, such as glucose, into usable energy in the form of ATP.
3. Mitochondria have an inner membrane that is highly folded, forming structures called cristae.
4. These cristae increase the surface area available for ATP production.
5. Within the mitochondria, there are various enzymes and proteins involved in the electron transport chain and ATP synthesis.

ATP Structure and Function:
1. ATP is composed of three main components: a sugar molecule called ribose, a nitrogenous base called adenine, and three phosphate groups.
2. The energy stored in ATP is primarily in the phosphate bonds.
3. When one phosphate group is cleaved from ATP, it forms Adenosine Diphosphate (ADP) and releases energy.
4. The energy released is used by the cell to perform various functions such as muscle contraction, active transport, and synthesis of macromolecules.

Role of ATP in Cellular Processes:
1. ATP is required for mechanical work, such as muscle contraction and movement of flagella and cilia.
2. It is involved in active transport processes, where molecules are transported against their concentration gradient.
3. ATP provides the energy required for biosynthetic reactions, including the synthesis of proteins, nucleic acids, and other macromolecules.
4. It plays a crucial role in signal transduction pathways, allowing cells to respond to external signals.
5. ATP is also involved in the maintenance of cell membrane potential and electrical signaling within the nervous system.

Conclusion:
The carrier of power synthesized by mitochondria is ATP. Mitochondria produce ATP through cellular respiration, and ATP serves as the primary energy currency within the cell. ATP provides energy for various cellular processes, including mechanical work, active transport, biosynthesis, and signal transduction.