To rewrite \( 100^{3/2} \) as a product of identical factors, we can use the properties of exponents.
First, we can express \( 100^{3/2} \) as:
\[ 100^{3/2} = (100^{1/2})^3 \]
Now, since \( 100^{1/2} \) is the square root of 100:
\[ 100^{1/2} = \sqrt{100} = 10 \]
Substituting this back into our expression, we get:
\[ 100^{3/2} = (10)^3 \]
Now, we can write \( 10^3 \) as a product of identical factors:
\[ 10^3 = 10 \times 10 \times 10 \]
So, the final product for \( 100^{3/2} \) is:
\[ 10 \times 10 \times 10 \]
Calculating \( 10^3 \):
\[ 10^3 = 1000 \]
Thus, the product for \( 100^{3/2} \) is \( 1000 \).