use the fact that 1.5 is the same as 3/2 to select all of the equations below that are equivalent to t =…

Explanation:

Step1: Substitute 1.5 with 3/2

Since 1.5 = 3/2, $T = A^{1.5}$ can be written as $T=A^{3/2}$.

Step2: Use exponent - rule $(a^m)^n=a^{mn}$

For $T=(A^{1/2})^3$, by the rule $(a^m)^n = a^{mn}$, we have $(A^{1/2})^3=A^{\frac{1}{2}\times3}=A^{3/2}$.

Step3: Recall the relationship between square - root and fractional exponent

We know that $A^{1/2}=\sqrt{A}$, so $(A^{1/2})^3 = (\sqrt{A})^3$ and also $A^{3/2}=\sqrt{A^3}$ (because $a^{m/n}=\sqrt[n]{a^m}$, when $n = 2$ and $m = 3$, $A^{3/2}=\sqrt{A^3}$).

Answer:

All of the options are correct.

• T = A^{3/2}
• T=(A^{1/2})^3
• T = (\sqrt{A})^3
• T=\sqrt{A^3}