Evaluate (15/21) Raised to the Negative Third Power: Step-by-Step Solution

To solve the expression $\left(\frac{15}{21}\right)^{-3}$, we will apply the rule for converting negative exponents into positive exponents.

Step 1: Recognize that the negative exponent indicates the reciprocal of the base raised to the positive equivalent of the exponent. Thus, we use the formula:

$\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$.

Step 2: Apply this formula to our expression:

$\left(\frac{15}{21}\right)^{-3} = \left(\frac{21}{15}\right)^3$.

Therefore, the solution to the problem is $\left(\frac{21}{15}\right)^3$, which corresponds to choice 3.