Rewrite the expression as a product of identical faction find the product of 100 3/2. Submit in simplified form

Answer 1

To rewrite the expression \( 100^{\frac{3}{2}} \) as a product of identical factors and find its value, we can follow these steps:

1. Rewrite \( 100^{\frac{3}{2}} \): \[ 100^{\frac{3}{2}} = (100^{\frac{1}{2}})^3 \]

2. Calculate \( 100^{\frac{1}{2}} \), which is the square root of 100: \[ 100^{\frac{1}{2}} = 10 \]

3. Now substitute this back into the expression: \[ (100^{\frac{1}{2}})^3 = (10)^3 \]

4. Calculate \( 10^3 \): \[ 10^3 = 1000 \]

Thus, the expression \( 100^{\frac{3}{2}} \) can be rewritten as \( (10)^3 \), and its simplified form is: \[ \boxed{1000} \]