To express the number \(2.8 \times 10^{-32.8}\) in standard form, we first need to rewrite the exponent in a more manageable form.
The term \(10^{-32.8}\) can be expressed as follows:
\[ 10^{-32.8} = \frac{1}{10^{32.8}} \]
Calculating \(10^{32.8}\) gives a very large number, and \(10^{-32.8}\) will represent a very small number. To convert it to standard form, we can adjust the exponent.
Recall that \(10^{-32.8}\) can be broken down:
\[ 10^{-32.8} = 10^{-32} \times 10^{-0.8} \]
Now, calculate \(10^{-0.8}\):
\[ 10^{-0.8} \approx 0.1585 \quad (\text{using a calculator}) \]
Now we combine the components:
\[ 2.8 \times 10^{-32.8} = 2.8 \times (10^{-32} \times 10^{-0.8}) = 2.8 \times 10^{-32} \times 0.1585 \]
Now we multiply \(2.8\) and \(0.1585\):
\[ 2.8 \times 0.1585 \approx 0.4438 \]
Thus, we can express our original term as:
\[ 0.4438 \times 10^{-32} \]
To rewrite this in proper scientific notation (standard form), we need to express \(0.4438\) as \(4.438\) multiplied by \(10^{-1}\):
\[ 0.4438 \times 10^{-32} = 4.438 \times 10^{-1} \times 10^{-32} = 4.438 \times 10^{-33} \]
So the final answer in standard form is:
\[ \boxed{4.438 \times 10^{-33}} \]