To rewrite the expression \(100^{32}\) as a product of identical factors, we can express it using rational exponents.
First, we identify that \(100\) can be expressed as \(10^2\). Thus, we have:
\[ 100^{32} = (10^2)^{32} \]
Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify:
\[ (10^2)^{32} = 10^{2 \cdot 32} = 10^{64} \]
Now, to express \(10^{64}\) as a product of identical factors:
\[ 10^{64} = 10 \times 10 \times 10 \times \ldots \times 10 \]
There would be \(64\) factors of \(10\).
Thus, \(100^{32}\) can be expressed as:
\[ 10^{64} \]
In simplified form, the answer is:
\[ 10^{64} \]