Evaluate (3/8)^(-5): Negative Exponents with Fractions

To solve this problem, we'll follow these steps:

• Step 1: Identify the given fraction and the negative exponent.
• Step 2: Apply the conversion rule from negative to positive exponents on fractions.

Now, let's work through each step:
Step 1: The given expression is $\left(\frac{3}{8}\right)^{-5}$. This indicates a fraction raised to a negative power.
Step 2: Applying the rule $(\frac{a}{b})^{-n} = (\frac{b}{a})^{n}$, we invert the fraction and change the exponent to positive. This gives us the expression $\left(\frac{8}{3}\right)^5$.

Therefore, the solution to the problem is $\left(\frac{8}{3}\right)^5$.