\( a^{2}=\frac{1}{25} \) \( b^{3}=a \) What is the value of \( b \) ? A \( \frac{1}{5} \) B \( \frac{1}{\sqrt{5}} \) C \( \frac{1}{\sqrt[3]{5}} \) D \( \sqrt[3]{5} \)

To solve for \( b \), we start with the equation given: 1. First, let's find \( a \) from the first equation: \[ a^{2} = \frac{1}{25} \] Taking the square root of both sides, we get: \[ a = \pm \frac{1}{5} \] 2. Now we use the second equation, \( b^{3} = a \). Let's consider the case where \( a = \frac{1}{5} \): \[ b^{3} = \frac{1}{5} \] Taking the cube root of both sides, we find: \[ b = \frac{1}{\sqrt[3]{5}} \] 3. If we consider the case where \( a = -\frac{1}{5} \), it would not yield a real number value for \( b \) since cube roots of negative numbers give a negative result. Thus, the only valid solution is: \[ b = \frac{1}{\sqrt[3]{5}} \] So, the value of \( b \) is: C \( \frac{1}{\sqrt[3]{5}} \)