Question

$\frac{ {12}^{\frac{1}{2} } }{ {3}^{ \frac{3}{2} } }$
Simplify this equation. The answer should be in a simplified equation form. ​

Answer 1

Answer:

The answer is $\dfrac{3}{2}$

Step-by-step explanation:

Given number is

 $\dfrac{(12)^{\frac{1}{2}}}{3^{\frac{3}{2}}}=\dfrac{(2^2\times 3)^{\frac{1}{2}}}{3^{1+\frac{1}{2}}}$

           $=\dfrac{(2^2)^{\frac{1}{2}}\times 3^{\frac{1}{2}}}{3^1\times 3^{\frac{1}{2}}}$ $\boxed{\because a^{m+n}=a^m\times a^n}$

            $=\dfrac{2^1}{3^1}$ $\boxed{\text{cancel common number from numerator and denominator}}$

            $=\dfrac{2}{3}$