To reduce the expression, we should start looking inside the parenthesis.
Let's look at [tex](5^{\frac{1}{8}}\times5^{\frac{3}{8}})[/tex]: there is a power property ("Power of a product property ") that says that when the bases of the products are equal, the following stands: [tex](5^{\frac{1}{8}}\times5^{\frac{3}{8}})=5^{(\frac{1}{8}+\frac{3}{8})} =5^{(\frac{4}{8})}=5^{(\frac{1}{2})}[/tex].
Now, we have to look at the resulting expression: [tex](5^{\frac{1}{2}})^3[/tex]. Because of the "Power of a power property", we can reduce this into [tex]5^{\frac{3}{2}}[/tex] (just by multiplying the powers).
The last expression is equivalent to [tex]\sqrt{5^3}[/tex], because when any number is rise at a certain fraction, the numerator of the fraction equals the power of the number, and the numerator of the fractiontells us the root index of the number (this means that, if you have a number "a" risen at a power "x/y" you can express it in two ways: [tex]a^{\frac{x}{y}}[/tex] or [tex]\sqrt[y]{a^x}[/tex])
