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

Question

. Submit your answer in simplified form and do not include a comma in your answer.(1 point)
​100^3/2=
​

Answer 1

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

1. Start with the base: \( 100 = 10^2 \).
2. Substitute that into the expression:
   \[ 100^{3/2} = (10^2)^{3/2} \]
3. Apply the power of a power property: \[ (10^2)^{3/2} = 10^{2 \cdot (3/2)} = 10^3 \]
4. Now, we have \( 10^3 \).

To express \( 10^3 \) as a product of identical factors: \[ 10^3 = 10 \times 10 \times 10 \]

Therefore, the simplified form of \( 100^{3/2} \) is:

\[ 10 \times 10 \times 10 \]

Thus, the final answer is:

\[ 10 \times 10 \times 10 \]