Find $\left(\sqrt{(\sqrt3)^3}\right)^4$.
I will start from the innermost expression and work my way outwards. Using the property that $(a^b)^c = a^{bc}$, I can rewrite this as $3^{3/2}$, which means the square root of 3 cubed. Using the same property as before, I can rewrite this as $3^{(3/2)(1/2)} = 3^{3/4}$, which means the fourth root of 3 cubed. Using the same property again, I can rewrite this as $3^{(3/4)(4)} = 3^3$, which is just 27. 