Question

5. Rewrite the expression as a product of identical
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 \( 1000 \).