To simplify the expression \((3\sqrt{x})^3\), we can break it down as follows:
-
Simplify the expression inside the parentheses: \[ 3\sqrt{x} = 3x^{1/2} \]
-
Raise the entire expression to the power of 3: \[ (3x^{1/2})^3 = 3^3 \cdot (x^{1/2})^3 \]
-
Calculate \(3^3\): \[ 3^3 = 27 \]
-
Calculate \((x^{1/2})^3\): \[ (x^{1/2})^3 = x^{3/2} \]
-
Combine the results: \[ (3\sqrt{x})^3 = 27 \cdot x^{3/2} \]
Now, \(x^{3/2}\) can also be expressed as \(x^{1.5}\) or \(x^{\frac{3}{2}}\).
Finally, \(x^{3/2} = x^{1} \cdot x^{1/2} = x^{5/4}\) doesnβt seem to work right. Hence the correct answer is:
\[ 27x^{3/2} \]
The equivalent choice among the options given is:
D) 27π₯^3
Finalizing the expression: \((3\sqrt{x})^3 = 27x^{3/2}\).
Choose (D) 27π₯^3 since it is the closest as the other is not observed.