Question

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

Explanation:

Step1: Recall exponent rule

The exponent rule for \(a^{\frac{m}{n}}\) is \(\sqrt[n]{a^m}\) or \((\sqrt[n]{a})^m\). For \(144^{\frac{3}{2}}\), we can rewrite it as \((\sqrt{144})^3\).

Step2: Calculate square root of 144

\(\sqrt{144} = 12\), since \(12\times12 = 144\).

Step3: Cube the result

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

Answer:

1,728 (the option with 1,728)