Respuesta :
Answer:
a) [tex]\frac{\sqrt[3]{6} }{\sqrt[4]{6} } = 6 ^{(\frac{1}{12}) [/tex]
Step-by-step explanation:
Here, the given expression is:
[tex]\frac{\sqrt[3]{6} }{\sqrt[4]{6} }[/tex]
Now, as we know that : [tex]\sqrt[a]{m} = m ^{(\frac{1}{a}) \\[/tex]
Applying same in the given expression, we get:
[tex]\sqrt[3]{6} = 6 ^{(\frac{1}{3})} \\\sqrt[4]{6} = 6 ^{(\frac{1}{4}) \\\implies \frac{\sqrt[3]{6} }{\sqrt[4]{6} }} \\ = \frac{6 ^{(\frac{1}{3})}}{ 6 ^{\frac{1}{4} }}[/tex]
Also, [tex]\frac{x ^m}{x^n} = x ^{(m-n)}[/tex]
Now, [tex]\frac{6 ^{(\frac{1}{3})}}{ 6 ^{\frac{1}{4} }} = 6 ^{(\frac{1}{3}) -(\frac{1}{4}) }} = 6 ^{(\frac{1}{12})[/tex]
Hence, [tex]\frac{\sqrt[3]{6} }{\sqrt[4]{6} } = 6 ^{(\frac{1}{12}) [/tex]
