To convert the equation [tex]\( T = A^{3/2} \)[/tex] into a form without any rational exponents, follow these steps:
1. Start with the given equation:
[tex]\[
T = A^{3/2}
\][/tex]
2. To eliminate the rational exponent, square both sides of the equation:
[tex]\[
(T)^2 = (A^{3/2})^2
\][/tex]
3. Applying the rule of exponents [tex]\((a^{m})^{n} = a^{m \cdot n}\)[/tex], we simplify the right-hand side:
[tex]\[
T^2 = (A^{3/2})^2
\][/tex]
[tex]\[
T^2 = A^{3}
\][/tex]
Thus, the equation in the form without any rational exponents is:
[tex]\[
T^2 = A^3
\][/tex]
This corresponds to the third option:
[tex]\[
T^2 - A^3
\][/tex]
