We can rewrite radicals as fractional exponents, like the following example
[tex]\sqrt[y]{x}=x^{\frac{1}{y}}[/tex]
Using this rule in our problem, we can rewrite our expression as
[tex]\sqrt[4]{5}\sqrt[16]{5}=5^{\frac{1}{4}}\cdot5^{\frac{1}{16}}[/tex]
When we have a product of two exponentials with the same basis, we just add the exponents.
[tex]a^b\cdot a^c=a^{b+c}[/tex]
Using this property in our problem, we have
[tex]5^{\frac{1}{4}}\cdot5^{\frac{1}{16}}=5^{\frac{1}{4}+\frac{1}{16}}=5^{\frac{4}{16}+\frac{1}{16}}=5^{\frac{5}{16}}=\sqrt[16]{5^5}=\sqrt[16]{3125}[/tex]
And this is our result.
[tex]\sqrt[4]{5}\sqrt[16]{5}=\sqrt[16]{3125}[/tex]
