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

To simplify the expression: \[ \frac{\left(y^{3}\right)^{6}}{y^{15}} \] follow these steps using the laws of exponents: ### Step 1: Apply the Power of a Power Rule The **Power of a Power** rule states that \((a^{m})^{n} = a^{m \times n}\). Apply this to \(\left(y^{3}\right)^{6}\): \[ \left(y^{3}\right)^{6} = y^{3 \times 6} = y^{18} \] ### Step 2: Rewrite the Expression Substitute \(y^{18}\) back into the original expression: \[ \frac{y^{18}}{y^{15}} \] ### Step 3: Apply the Quotient Rule The **Quotient** rule for exponents states that \(\frac{a^{m}}{a^{n}} = a^{m - n}\). Apply this to \(\frac{y^{18}}{y^{15}}\): \[ \frac{y^{18}}{y^{15}} = y^{18 - 15} = y^{3} \] ### Final Simplified Form \[ y^{3} \] **Therefore, the simplified form of \(\frac{\left(y^{3}\right)^{6}}{y^{15}}\) is \(y^{3}\).**