5. Rewrite the expression as a product of identical

Question

factors to find the product for
100
3/2

Answer 1

To rewrite the expression \( 100^{3/2} \) as a product of identical factors, we can break it down as follows:

1. First, rewrite \( 100^{3/2} \):

   \[ 100^{3/2} = (100^{1/2})^3 \]

2. Calculate \( 100^{1/2} \), which is the square root of \( 100 \):

   \[ 100^{1/2} = 10 \]

3. Now, substitute \( 10 \) back into the equation:

   \[ (100^{1/2})^3 = (10)^3 \]

4. Finally, calculate \( (10)^3 \):

   \[ 10^3 = 10 \times 10 \times 10 = 1000 \]

Thus, \( 100^{3/2} \) can be expressed as \( (10)^3 \), and the product is \( 1000 \).