Answer:
[tex]\sqrt[20]{3}[/tex]
Step-by-step explanation:
Using the radical rule ([tex]\sqrt[x]{a}=a^{\frac{1}{x}[/tex]), we can rewrite the fraction:
(3^1/4)/(3^1/5)
Since we are dividing exponents with the same base, we can subtract the two exponents to get:
3^(1/4-1/5)
Convert both fractions to a base of 20:
[tex]\frac{1}{4}*\frac{5}{5}=\frac{5}{20}[/tex] (notice we can only multiply by a number of itself since it is essentially like multiplying the fraction by 1)
[tex]\frac{1}{5}*\frac{4}{4}=\frac{4}{20}[/tex]
Therefore we have:
3^(5/20-4/20)=3^(1/20)
Which again using the radical rule we can rewrite as:
[tex]\sqrt[20]{3}[/tex]
