which expression is equivalent to $144^{\frac{3}{2}}$?\n216\n1,728\n$sqrt3{12}$\n$sqrt3{72}$

Explanation:

Step1: Rewrite the exponent form

We know that $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}=( \sqrt[n]{a})^{m}$. For $144^{\frac{3}{2}}$, we can rewrite it as $(\sqrt{144})^{3}$.

Step2: Calculate the square - root

Since $\sqrt{144} = 12$ (because $12\times12 = 144$), then $(\sqrt{144})^{3}=12^{3}$.

Step3: Calculate the cube

$12^{3}=12\times12\times12 = 1728$.

Answer:

1,728