Convert the equation you found, [tex]$T=A^{3 / 2}$[/tex], into a form without any rational exponents.

A. [tex]T^2=A^3[/tex]
B. [tex]\frac{1}{2} T=A^3[/tex]
C. [tex]T^2-A^3[/tex]
D. [tex]T^2=\frac{1}{3} A[/tex]



Answer :

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]