\( \left. \begin{array} { l } { | \leftarrow \quad \left. \begin{array} { l } { \frac { y ^ { 9 } } { y ^ { 6 } } } \\ { \frac { y ^ { 9 } } { y ^ { 6 } } = \square } \end{array} \right. } \end{array} \right. \)

To simplify the expression \( \frac{y^9}{y^6} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). Apply this property here: \[ \frac{y^9}{y^6} = y^{9-6} = y^3. \] So, the answer is \( y^3 \). In practical terms, understanding how to work with exponents is incredibly useful, especially in fields like physics and engineering. For example, when calculating the area or volume of geometric shapes, you often rely on these exponent rules. Whether scaling dimensions or converting units, having a solid grip on exponents can make complex problems much simpler! Many students often mistakenly try to directly divide the bases without applying the exponent rules. This can lead to errors when they incorrectly simplify expressions, resulting in misunderstanding how the properties of exponents work. Always remember to subtract the exponents for division to stay on the right track!