For this case we have to define properties of powers and roots that:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So, if we have the following expression:
[tex]27 ^ {\frac {1} {5}}[/tex]
We can rewrite it as:
[tex]\sqrt [5] {27 ^ 1} = \sqrt [5] {27}[/tex]
ANswer:
[tex]\sqrt [5] {27}[/tex]
Answer:
The required expression is [tex]27^{\frac{1}{5} } = \sqrt[5]{27}[/tex] or [tex]27^{\frac{1}{5} } = \sqrt[5]{3^3}[/tex]
Step-by-step explanation:
Consider the provided expression : [tex]27^{(\frac{1}{5} )}[/tex]
We need to find the radical expression.
Use the property:
[tex]\sqrt[n]{x} = x^\frac{1}{n}[/tex]
Where n is the index of the radical.
By using the above property we can rewrite the above expression as:
[tex]27^{\frac{1}{5} } = \sqrt[5]{27}[/tex]
OR
We can write 27 = 3×3×3 = 3³
[tex]\sqrt[5]{27} = \sqrt[5]{3^3}[/tex]
Therefore, the required expression is [tex]27^{\frac{1}{5} } = \sqrt[5]{27}[/tex] or [tex]27^{\frac{1}{5} } = \sqrt[5]{3^3}[/tex]
