Questions: (-32)^(-3/5)

Solution Steps

We start with the expression \((-32)^{-\frac{3}{5}}\). According to the negative exponent rule, we can rewrite this as: \[ (-32)^{-\frac{3}{5}} = \frac{1}{(-32)^{\frac{3}{5}}} \]

Next, we need to evaluate \((-32)^{\frac{3}{5}}\). This can be broken down into two parts: first, we take the fifth root of \(-32\), and then we raise the result to the power of \(3\): \[ (-32)^{\frac{3}{5}} = \left((-32)^{\frac{1}{5}}\right)^3 \]

The fifth root of \(-32\) is \(-2\) because \((-2)^5 = -32\). Therefore, we have: \[ (-32)^{\frac{3}{5}} = (-2)^3 = -8 \] Substituting this back into our expression gives: \[ (-32)^{-\frac{3}{5}} = \frac{1}{-8} = -0.125 \]

Final Answer