Step-by-step explanation:
So, the question is asking for us to find [tex](ab)^{\frac{3}{2} }[/tex].
Let's find a and b, then plug it into the expression.
[tex]\frac{a}{3+\sqrt{5} } = \frac{3-\sqrt{5} }{b} \\\\Multiply//3+\sqrt{5} * both//sides\\a = \frac{(3+\sqrt{5} )*(3-\sqrt{5} )}{b} \\\\Solve\\a = \frac{4}{b}\\ Do//the//same//steps//but//for//b\\The//answer//for//b//is:\\b = \frac{4}{a} \\Now//insert//into//expression\\((\frac{4}{b})(\frac{4}{a}))^{\frac{3}{2} } \\\\\frac{64}{b^{\frac{3}{2} }a^{\frac{3}{2} } }[/tex]
