To find the combined diameter of the body cell and plant cell, we need to add the diameters of both cells.
The average diameter of the human body cell is given as: \[ 5.1 \cdot 10^{-4} \text{ cm} \]
The diameter of the plant cell is given as: \[ 8 \cdot 10^{-3} \text{ cm} \]
Before adding these two numbers, we will convert them to the same exponent in scientific notation. The smaller exponent is \(10^{-4}\), so we will convert \(8 \cdot 10^{-3}\) to have the same exponent:
\[ 8 \cdot 10^{-3} = 80 \cdot 10^{-4} \quad \text{(since } 8 = 80 \times 10^{-1} \text{)} \]
Now, we can add: \[ 5.1 \cdot 10^{-4} + 80 \cdot 10^{-4} = (5.1 + 80) \cdot 10^{-4} = 85.1 \cdot 10^{-4} \]
To express this in proper scientific notation, we must write \(85.1\) as \(8.51 \cdot 10^1\), which means: \[ 85.1 \cdot 10^{-4} = 8.51 \cdot 10^{1} \cdot 10^{-4} = 8.51 \cdot 10^{-3} \]
Therefore, the combined diameter of the body cell and plant cell in scientific notation is: \[ \boxed{8.51 \cdot 10^{-3}} \text{ cm} \]