Answer:
[tex](2\cdot 6)^{\frac{3}{2}}=24(3)^{\frac{1}{2}}[/tex]
Step-by-step explanation:
The given expression is [tex](2*6)^{\frac{3}{2}}[/tex]
We multiply within the parenthesis to get:
[tex](12)^{\frac{3}{2}}[/tex]
Recall that: [tex]a^{\frac{m}{n} } =\sqrt[n]{x^m}[/tex]
We apply this property to get:
[tex](12)^{\frac{3}{2}}=\sqrt{12^3}[/tex]
[tex](12)^{\frac{3}{2}}=\sqrt{12^2*12}[/tex]
This simplifies to
[tex](12)^{\frac{3}{2}}=12\sqrt{12}[/tex]
We can simplify further
[tex](12)^{\frac{3}{2}}=12\sqrt{4*3}=12*2\sqrt{3}=24\sqrt{3}[/tex]
We rewrite as rational exponent [tex]24(3)^{\frac{1}{2}}[/tex]
