b) \( \frac{\left(y^{3}\right)^{6}}{y^{15}} \)

First, let's simplify the expression \(\frac{\left(y^{3}\right)^{6}}{y^{15}}\). By applying the power of a power rule, we can simplify \(\left(y^{3}\right)^{6}\) to \(y^{18}\). So now we have \(\frac{y^{18}}{y^{15}}\). When dividing like bases, we subtract the exponents: \(18 - 15 = 3\). Therefore, the simplified expression is \(y^{3}\). Isn't it fascinating how exponents can make these calculations quicker? Remember, keeping your exponent rules in mind can save you a lot of time and effort when tackling algebraic expressions! You can also think of exponents as a shorthand notation that helps represent repeated multiplication—perfect for efficiently working with large numbers or variables!