Question

which expression is equivalent to $144^{\frac{3}{2}}$?
1,728
216
$sqrt3{72}$
$sqrt3{12}$

Explanation:

Step 1: Recall the exponent rule for \(a^{\frac{m}{n}}\)

The formula for a fractional exponent \(a^{\frac{m}{n}}\) is \(\sqrt[n]{a^m}\) or \((\sqrt[n]{a})^m\). So for \(144^{\frac{3}{2}}\), we can rewrite it as \((\sqrt{144})^3\) (using the form \((\sqrt[n]{a})^m\) where \(n = 2\), \(m=3\), \(a = 144\)).

Step 2: Calculate \(\sqrt{144}\)

We know that \(\sqrt{144}=12\) because \(12\times12 = 144\).

Step 3: Calculate \(12^3\)

Now we need to find \(12^3\). \(12^3=12\times12\times12\). First, \(12\times12 = 144\), then \(144\times12=1728\).

Answer:

\(1,728\) (the option with the value \(1,728\))