Question: Evaluate the expression.
Do not round your answer.
\[\dfrac{17}{6^2}-\dfrac{5}{9\cdot4}=\]
1. **State the problem:** Evaluate the expression $$\dfrac{17}{6^2} - \dfrac{5}{9 \cdot 4}$$ without rounding the answer.
2. **Recall the formula and rules:** We need to simplify each fraction and then subtract. Remember that $$6^2 = 6 \times 6 = 36$$ and multiplication in the denominator is straightforward.
3. **Calculate each denominator:**
$$6^2 = 36$$
$$9 \cdot 4 = 36$$
4. **Rewrite the expression with denominators:**
$$\dfrac{17}{36} - \dfrac{5}{36}$$
5. **Since denominators are the same, subtract numerators:**
$$\dfrac{17 - 5}{36}$$
6. **Simplify numerator:**
$$\dfrac{12}{36}$$
7. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD), which is 12:**
$$\dfrac{\cancel{12}^1}{\cancel{36}^3}$$
8. **Final simplified answer:**
$$\dfrac{1}{3}$$
Thus, the value of the expression is $$\dfrac{1}{3}$$.