For what values of the variable of the following g expression make sense?

To the power of ^3 square root of a

1 answer

To analyze the expression you've provided, which looks like it can be interpreted as \( \sqrt[3]{\sqrt{a}} \) (the cube root of the square root of \( a \)), we need to consider the values of \( a \) for which this expression is defined.

  1. Square Root (\( \sqrt{a} \)): The square root of \( a \) is defined for \( a \geq 0 \). Therefore, \( a \) must be non-negative.

  2. Cube Root (\( \sqrt[3]{x} \)): The cube root is defined for all real numbers, so there are no additional restrictions from this part.

Putting these points together, the only restriction on \( a \) comes from the square root:

  • The expression \( \sqrt[3]{\sqrt{a}} \) makes sense for \( a \geq 0 \).

In summary, the valid values for \( a \) that make the expression \( \sqrt[3]{\sqrt{a}} \) defined are:

\[ a \geq 0 \]