Answer: [tex]24\sqrt{3}[/tex]
Step-by-step explanation:
You need to remember that [tex]\sqrt[n]{a}[/tex] can be written in the following for:
[tex]a^{\frac{1}{n}}[/tex]
Knowing this and given the expression [tex](2*6)^{\frac{3}{2}}[/tex], you need to multiply the numbers inside the parentheses:
[tex](12)^{\frac{3}{2}}[/tex]
Rewrite it in this form:
[tex]=\sqrt{12^3}==\sqrt{1,728}[/tex]
Descompose 1,728 into its prime factors:
[tex]1,728=2*2*2*2*2*2*3*3*3=2^6*3^3[/tex]
Applying the Product of power property, which states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
You can say that:
[tex]=\sqrt{1,728}=\sqrt{2^6*3^2*3}[/tex]
Simplifying, you get:
[tex]=2^3*3\sqrt{3}=24\sqrt{3}[/tex]
