Rewrite the expression as a product of identical factors to find the product for 100^3/2

Question

. Submit your answer in simplified form.

Answer 1

To simplify the expression \( 100^{3/2} \), we can rewrite it as follows:

1. First, express \( 100 \) as \( 10^2 \):

\[ 100^{3/2} = (10^2)^{3/2} \]

2. Use the power of a power property, which states \( (a^m)^n = a^{m \cdot n} \):

\[ (10^2)^{3/2} = 10^{2 \cdot (3/2)} = 10^3 \]

3. Now, compute \( 10^3 \):

\[ 10^3 = 1000 \]

Therefore, the product of identical factors of \( 100^{3/2} \) is \( 1000 \).

So the simplified form is:

\[ \boxed{1000} \]