Question

rewrite the expression as a product of identical factors to find the product for 100^3/2, simplify the answer

Answer 1

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

1. Start by expressing \( 100 \) as a power of \( 10 \):
\[
100 = 10^2
\]

2. Substitute \( 100 \) in the expression:
\[
100^{3/2} = (10^2)^{3/2}
\]

3. Use the power of a power property \( (a^m)^n = a^{m \cdot n} \):
\[
(10^2)^{3/2} = 10^{2 \cdot (3/2)} = 10^3
\]

4. Now we can simplify \( 10^3 \):
\[
10^3 = 1000
\]

Thus, the expression \( 100^{3/2} \) simplifies to \( 1000 \).

If you specifically want to express it as a product of identical factors, we can write \( 1000 \) as:
\[
1000 = 10 \times 10 \times 10
\]

So, the simplified answer is:
\[
1000
\] or written as a product of identical factors:
\[
10^3
\]