(d) \( \frac{3^{2} \times\left(p^{-2}\right)^{3} \times\left(q^{-1}\right)^{0} \times\left(p^{3}\right)^{-2}}{3^{-1} \times\left(p^{-1}\right)^{-1} \times\left(q^{5}\right)^{2}}(p \neq 0, q \neq 0) \)

Calculate or simplify the expression \( 3^{2} \times (p^{-2})^{3} \times (q^{-1})^{0} \times (p^{3})^{-2} / (3^{-1} \times (p^{-1})^{-1} \times (q^{5})^{2}) \). Simplify the expression by following steps: - step0: Solution: \(\frac{3^{2}\left(p^{-2}\right)^{3}\left(q^{-1}\right)^{0}\left(p^{3}\right)^{-2}}{\left(3^{-1}\left(p^{-1}\right)^{-1}\left(q^{5}\right)^{2}\right)}\) - step1: Remove the parentheses: \(\frac{3^{2}\left(p^{-2}\right)^{3}\left(q^{-1}\right)^{0}\left(p^{3}\right)^{-2}}{3^{-1}\left(p^{-1}\right)^{-1}\left(q^{5}\right)^{2}}\) - step2: Multiply by \(a^{-n}:\) \(\frac{3^{2}\left(p^{-2}\right)^{3}\left(q^{-1}\right)^{0}\left(p^{3}\right)^{-2}\times 3}{\left(p^{-1}\right)^{-1}\left(q^{5}\right)^{2}}\) - step3: Multiply the exponents: \(\frac{3^{2}\left(p^{-2}\right)^{3}\left(q^{-1}\right)^{0}\left(p^{3}\right)^{-2}\times 3}{\left(p^{-1}\right)^{-1}q^{5\times 2}}\) - step4: Multiply the exponents: \(\frac{3^{2}\left(p^{-2}\right)^{3}\left(q^{-1}\right)^{0}\left(p^{3}\right)^{-2}\times 3}{p^{-\left(-1\right)}q^{5\times 2}}\) - step5: Multiply the exponents: \(\frac{3^{2}\left(p^{-2}\right)^{3}\left(q^{-1}\right)^{0}p^{3\left(-2\right)}\times 3}{p^{-\left(-1\right)}q^{5\times 2}}\) - step6: Multiply by \(a^{-n}:\) \(\frac{3^{2}\left(p^{-2}\right)^{3}\left(q^{-1}\right)^{0}p^{3\left(-2\right)}\times 3p^{1\times \left(-1\right)}}{q^{5\times 2}}\) - step7: Multiply the exponents: \(\frac{3^{2}p^{-2\times 3}\left(q^{-1}\right)^{0}p^{3\left(-2\right)}\times 3p^{1\times \left(-1\right)}}{q^{5\times 2}}\) - step8: Multiply the numbers: \(\frac{3^{2}p^{-6}\left(q^{-1}\right)^{0}p^{3\left(-2\right)}\times 3p^{1\times \left(-1\right)}}{q^{5\times 2}}\) - step9: Multiply the numbers: \(\frac{3^{2}p^{-6}\left(q^{-1}\right)^{0}p^{-6}\times 3p^{1\times \left(-1\right)}}{q^{5\times 2}}\) - step10: Calculate: \(\frac{3^{2}p^{-6}\left(q^{-1}\right)^{0}p^{-6}\times 3p^{-1}}{q^{5\times 2}}\) - step11: Evaluate the power: \(\frac{3^{2}p^{-6}\times 1\times p^{-6}\times 3p^{-1}}{q^{5\times 2}}\) - step12: Multiply the numbers: \(\frac{3^{2}p^{-6}\times 1\times p^{-6}\times 3p^{-1}}{q^{10}}\) - step13: Multiply the terms: \(\frac{3^{3}p^{-13}}{q^{10}}\) - step14: Rewrite the expression: \(\frac{\frac{3^{3}}{p^{13}}}{q^{10}}\) - step15: Simplify: \(\frac{3^{3}}{q^{10}p^{13}}\) - step16: Evaluate the power: \(\frac{27}{q^{10}p^{13}}\) The simplified expression is \( \frac{27}{q^{10}p^{13}} \).