To write the expression [tex]\( 36^{3/2} \)[/tex] in radical form and then evaluate it, we follow these steps:
1. Convert the expression to radical form:
The exponent [tex]\( 3/2 \)[/tex] can be interpreted as a combination of a root and a power. Specifically:
[tex]\[
36^{3/2} = (\sqrt{36})^3
\][/tex]
Here, [tex]\( \sqrt{36} \)[/tex] represents the square root of 36, and the cube (or third power) is applied to the result of the square root.
2. Evaluate the square root:
[tex]\[
\sqrt{36} = 6
\][/tex]
3. Apply the cube (third power):
[tex]\[
6^3 = 6 \times 6 \times 6 = 216
\][/tex]
Thus, the simplified answer is [tex]\( 36^{3/2} = 216 \)[/tex].
So, the correct choice is:
A. [tex]\( 36^{3/2} = 216 \)[/tex]
