. 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 first express \( 100 \) in a more manageable form.

We know that:

\[ 100 = 10^2 \]

So,

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

Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify this:

\[ (10^2)^{3/2} = 10^{2 \cdot \frac{3}{2}} = 10^{3} \]

Now, \( 10^{3} = 10 \times 10 \times 10\).

Thus, \( 100^{3/2} = 10 \times 10 \times 10 \).

In simplified form:

\[ \boxed{10 \times 10 \times 10} \] or, if you need a single result, \( 1000 \).