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