Answer:
See explanation below
Step-by-step explanation:
First we will going to rewrite 54 into its prime factors: 54 = 3³(2)
So, the expression [tex]\frac{3\sqrt{54} }{3\sqrt{2} }[/tex] can be written as:
[tex]\frac{3\sqrt{3^32} }{3\sqrt{2} } =\frac{3(3^{3/2})2^{1/2} }{3(2^{1/2}) } =3^{3/2}=3\sqrt{3}[/tex]
*We used the fact that a square root is like having a 1/2 exponent so we multiplied the exponents inside the root by 1/2 and then simplified them*
