Question

What is the radical expression that is equivalent 27 1/5?

Answer 1

For this case we have to define properties of powers and roots that:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

So, if we have the following expression:

$27 ^ {\frac {1} {5}}$

We can rewrite it as:

$\sqrt [5] {27 ^ 1} = \sqrt [5] {27}$

ANswer:

$\sqrt [5] {27}$

Answer 2

Answer:

The required expression is $27^{\frac{1}{5} } = \sqrt[5]{27}$ or $27^{\frac{1}{5} } = \sqrt[5]{3^3}$

Step-by-step explanation:

Consider the provided expression : $27^{(\frac{1}{5} )}$

We need to find the radical expression.

Use the property:

$\sqrt[n]{x} = x^\frac{1}{n}$

Where n is the index of the radical.

By using the above property we can rewrite the above expression as:

$27^{\frac{1}{5} } = \sqrt[5]{27}$

OR

We can write 27 = 3×3×3 = 3³

$\sqrt[5]{27} = \sqrt[5]{3^3}$

Therefore, the required expression is $27^{\frac{1}{5} } = \sqrt[5]{27}$ or $27^{\frac{1}{5} } = \sqrt[5]{3^3}$