Precalculus: Mathematics for Calculus, 7th Edition

4$^{3/2}$ = ($\sqrt[2] 4$)$^{3}$ by definition. We are here elevating 4 to the power of 3/2. We can do this in the two following ways: 4$^{3/2}$=(4$^{1/2}$)$^{3}$ = 2$^{3}$ = 8 4$^{3/2}$=(4$^{3}$)$^{1/2}$= 64$^{1/2}$= 8
Taking the square root of a number is equivalent to elevating that number to the 1/2 power. Which is why we can use Law 3 which states: (a$^{m}$)$^{n}$= (a$^{n}$)$^{m}$= a$^{mn}$. We note that the powers n and m are interchangeable.