Answer:
[tex]5^{\frac{1}{12}}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{\sqrt[3]{5} }{\sqrt[4]{5} }[/tex]
To simplify this expression we need to apply the exponent property that allows to transform from radical expression to a power with a fraction exponent, the property states:
[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]
Applying the property we have:
[tex]\frac{\sqrt[3]{5} }{\sqrt[4]{5} }\\\frac{(5)^{\frac{1}{3} } }{(5)^{\frac{1}{4} } } \\5^{\frac{1}{3}-\frac{1}{4}}=5^{\frac{4-3}{12}}=5^{\frac{1}{12}}[/tex]
Therefore, the simplified expression is [tex]5^{\frac{1}{12}}[/tex]
