Question

Simplify (Look at the picture) No links please

Answer 1

Answer:

$\sqrt[20]{3}$

Step-by-step explanation:

Using the radical rule ($\sqrt[x]{a}=a^{\frac{1}{x}$), 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:

$\frac{1}{4}*\frac{5}{5}=\frac{5}{20}$ (notice we can only multiply by a number of itself since it is essentially like multiplying the fraction by 1)

$\frac{1}{5}*\frac{4}{4}=\frac{4}{20}$

Therefore we have:

3^(5/20-4/20)=3^(1/20)

Which again using the radical rule we can rewrite as:

$\sqrt[20]{3}$

Answer 2

Answer:

$\frac{\sqrt[4]{3}}{ \sqrt[5]{3} } = \frac{ {3}^{ \frac{1}{4} } }{ {3}^{ \frac{1}{5} } } \\ = {3}^{ \frac{1}{4} - \frac{1}{5} } \\ = {3}^{ \frac{5}{20} - \frac{4}{20} } \\ = {3}^{ \frac{1}{20} } \: or \: \sqrt[20]{3}$