Evaluate (10/17)^(-5): Negative Exponent Fraction Problem

To solve the problem, we will follow these steps:

• Step 1: Identify the expression and apply the rule for negative exponents.
• Step 2: Take the reciprocal of the given fraction $\frac{10}{17}$.
• Step 3: Raise the reciprocal to the positive power of 5.

Now, let's work through each step:
Step 1: We start with the problem expression $\left(\frac{10}{17}\right)^{-5}$. According to the laws of exponents, a negative exponent means the reciprocal of the base should be raised to the positive of that exponent.
Step 2: Take the reciprocal of $\frac{10}{17}$, which is $\frac{17}{10}$.
Step 3: Raise the reciprocal $\frac{17}{10}$ to the power of 5, resulting in $\left(\frac{17}{10}\right)^5$.

Therefore, the equivalent expression is $\left(\frac{17}{10}\right)^5$.