Question

use the properties of rational exponents. be sure your answer is in simplest form.
$(2 \cdot 6)^{\frac{3}{2}}$

Explanation:

Step1: Multiply inside the parentheses

$2 \cdot 6 = 12$
So the expression becomes $12^{\frac{3}{2}}$

Step2: Rewrite using exponent rules

Recall $a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$. For $12^{\frac{3}{2}}$, this is $(\sqrt{12})^3$

Step3: Simplify the square root

$\sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3}$

Step4: Cube the simplified root

$(2\sqrt{3})^3 = 2^3 \cdot (\sqrt{3})^3 = 8 \cdot 3\sqrt{3}$

Step5: Multiply the constants

$8 \cdot 3 = 24$

Answer:

$24\sqrt{3}$