Question

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

Answer 1

To rewrite \( 100^{3/2} \) as a product of identical factors, we can use the properties of exponents.

First, we can express \( 100^{3/2} \) as:

\[
100^{3/2} = (100^{1/2})^3
\]

Now, since \( 100^{1/2} \) is the square root of 100:

\[
100^{1/2} = \sqrt{100} = 10
\]

Substituting this back into our expression, we get:

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

Now, we can write \( 10^3 \) as a product of identical factors:

\[
10^3 = 10 \times 10 \times 10
\]

So, the final product for \( 100^{3/2} \) is:

\[
10 \times 10 \times 10
\]

Calculating \( 10^3 \):

\[
10^3 = 1000
\]

Thus, the product for \( 100^{3/2} \) is \( 1000 \).