Question

which expression is equivalent to ( 144^{\frac{3}{2}} )?
( circ ) 216
( circ ) 1728
( circ ) ( sqrt3{12} )
( circ ) ( sqrt3{72} )

Explanation:

Step1: Recall exponent rule

For \(a^{\frac{m}{n}}\), it can be rewritten as \((\sqrt[n]{a})^m\) or \(\sqrt[n]{a^m}\). Here, \(a = 144\), \(m = 3\), \(n = 2\).

Step2: Simplify the exponent

First, handle the denominator of the fraction in the exponent. \(\sqrt[2]{144}=12\) (since \(12\times12 = 144\)).

Step3: Raise the result to the power of 3

Now, raise 12 to the power of 3: \(12^3=12\times12\times12 = 1728\).

Answer:

1728 (the option with the value 1728)