Question

Simplest form to write (2×6)³/²

Answer 1

Answer: $24\sqrt{3}$

Step-by-step explanation:

You need to remember that $\sqrt[n]{a}$ can be written in the following for:

$a^{\frac{1}{n}}$

Knowing this and given the expression $(2*6)^{\frac{3}{2}}$, you need to  multiply the numbers inside the parentheses:

 $(12)^{\frac{3}{2}}$

Rewrite it in this form:

$=\sqrt{12^3}==\sqrt{1,728}$

Descompose 1,728 into its prime factors:

$1,728=2*2*2*2*2*2*3*3*3=2^6*3^3$

Applying the Product of power property, which states that:

$(a^m)(a^n)=a^{(m+n)}$

You can say that:

 $=\sqrt{1,728}=\sqrt{2^6*3^2*3}$

Simplifying, you get:

$=2^3*3\sqrt{3}=24\sqrt{3}$