the mitochrondria is the powerhouse of the cell
Yes.
Introduction
A mitochondrion is thus termed the "powerhouse" of the cell.

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Mitochondrion
Function
The most prominent roles of mitochondria are to produce the energy currency of the cell, ATP (i.e., phosphorylation of ADP), 
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Mitochondrion [SEP] Introduction
Mitochondria generate most of the cell's supply of adenosine triphosphate (ATP), used as a source of chemical energy. A mitochondrion is thus termed the "powerhouse" of the cell. Mitochondria are commonly between 0.75 and 3 μm² in area but vary considerably in size and structure. Unless specifically stained, they are not visible. In addition to supplying cellular energy, mitochondria are involved in other tasks, such as signaling, cellular differentiation, and cell death, as well as maintaining control of the cell cycle and cell growth. Mitochondrial biogenesis is in turn temporally coordinated with these cellular processes. Mitochondria have been implicated in several human diseases, such as mitochondrial disorders, cardiac dysfunction, heart failure and autism.