Final answer:
To convert the equation without rational exponents, you can square both sides, resulting in the equation t² = a³, which is the original equation without rational exponents.
Step-by-step explanation:
The equation t = a³/² uses a rational exponent, which might be a bit confusing. To convert this equation into a form without any rational exponents, we can utilize the property that tells us that the square root of a number can also be expressed as the number raised to the power of 1/2. Furthermore, to raise a number to a cube, we would raise it to the power of 3. So in this case for the expression a³, we are looking at the cube of a, and the expression a³/² indicates the square root of a³, which can also be written as a raised to the power of 3/2.
Algebraically speaking, if t is equal to the square root of a³, then t squared (t²) must be equal to a³, because squaring a number is the inverse operation of taking the square root. Therefore, the conversion of the original equation t = a³/² without rational exponents would be t² = a³.