(1.) \( \frac{\left(x^{2} y^{3} z^{-6}\right)\left(a^{5} x^{4} z^{3}\right)}{\left(a^{2} x^{3} y^{2} z^{6}\right)} \) (2) \( \frac{\left(a^{-2} b^{5} c^{6} y^{9}\right)\left(a^{-4} b^{3} x^{6} z^{8}\right)}{\left(a^{6} c^{-3} x^{-4} z^{3}\right)} \) (3) \( \frac{\left(x^{6} y^{7} z^{8}\right)\left(x^{3} y^{2} z^{1}\right)\left(a^{6} b^{4}\right.}{\left(a^{2} b^{4} c^{6}\right)\left(x^{1} y^{2} z^{3}\right)\left(x^{8} y^{7}\right.} \)

Simplify the expression by following steps: - step0: Solution: \(\frac{\left(x^{2}y^{3}z^{-6}\right)\left(a^{5}x^{4}z^{3}\right)}{\left(a^{2}x^{3}y^{2}z^{6}\right)}\) - step1: Evaluate: \(\frac{\left(x^{2}y^{3}z^{-6}\right)a^{5}x^{4}z^{3}}{a^{2}x^{3}y^{2}z^{6}}\) - step2: Remove the parentheses: \(\frac{x^{2}y^{3}z^{-6}a^{5}x^{4}z^{3}}{a^{2}x^{3}y^{2}z^{6}}\) - step3: Multiply: \(\frac{x^{6}y^{3}z^{-3}a^{5}}{a^{2}x^{3}y^{2}z^{6}}\) - step4: Reduce the fraction: \(\frac{x^{3}ya^{3}}{z^{9}}\) Calculate or simplify the expression \( (x^{6} y^{7} z^{8})(x^{3} y^{2} z^{1})(a^{6} b^{4})/((a^{2} b^{4} c^{6})(x^{1} y^{2} z^{3})(x^{8} y^{7})) \). Simplify the expression by following steps: - step0: Solution: \(\frac{x^{6}y^{7}z^{8}x^{3}y^{2}za^{6}b^{4}}{\left(a^{2}b^{4}c^{6}xy^{2}z^{3}x^{8}y^{7}\right)}\) - step1: Remove the parentheses: \(\frac{x^{6}y^{7}z^{8}x^{3}y^{2}za^{6}b^{4}}{a^{2}b^{4}c^{6}xy^{2}z^{3}x^{8}y^{7}}\) - step2: Multiply: \(\frac{x^{9}y^{9}z^{9}a^{6}b^{4}}{a^{2}b^{4}c^{6}xy^{2}z^{3}x^{8}y^{7}}\) - step3: Multiply: \(\frac{x^{9}y^{9}z^{9}a^{6}b^{4}}{a^{2}b^{4}c^{6}x^{9}y^{9}z^{3}}\) - step4: Reduce the fraction: \(\frac{z^{6}a^{4}}{c^{6}}\) Calculate or simplify the expression \( (a^{-2} b^{5} c^{6} y^{9})(a^{-4} b^{3} x^{6} z^{8})/(a^{6} c^{-3} x^{-4} z^{3}) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(a^{-2}b^{5}c^{6}y^{9}\right)\left(a^{-4}b^{3}x^{6}z^{8}\right)}{\left(a^{6}c^{-3}x^{-4}z^{3}\right)}\) - step1: Remove the parentheses: \(\frac{a^{-2}b^{5}c^{6}y^{9}a^{-4}b^{3}x^{6}z^{8}}{a^{6}c^{-3}x^{-4}z^{3}}\) - step2: Multiply by \(a^{-n}:\) \(a^{-2}b^{5}c^{6}y^{9}a^{-4}b^{3}x^{6}z^{8}a^{-6}c^{3}x^{4}z^{-3}\) - step3: Multiply the terms: \(a^{-2-4-6}b^{5}c^{6}y^{9}b^{3}x^{6}z^{8}c^{3}x^{4}z^{-3}\) - step4: Subtract the numbers: \(a^{-12}b^{5}c^{6}y^{9}b^{3}x^{6}z^{8}c^{3}x^{4}z^{-3}\) - step5: Multiply the terms: \(a^{-12}b^{5+3}c^{6}y^{9}x^{6}z^{8}c^{3}x^{4}z^{-3}\) - step6: Add the numbers: \(a^{-12}b^{8}c^{6}y^{9}x^{6}z^{8}c^{3}x^{4}z^{-3}\) - step7: Multiply the terms: \(a^{-12}b^{8}c^{6+3}y^{9}x^{6}z^{8}x^{4}z^{-3}\) - step8: Add the numbers: \(a^{-12}b^{8}c^{9}y^{9}x^{6}z^{8}x^{4}z^{-3}\) - step9: Multiply the terms: \(a^{-12}b^{8}c^{9}y^{9}x^{6+4}z^{8}\times z^{-3}\) - step10: Add the numbers: \(a^{-12}b^{8}c^{9}y^{9}x^{10}z^{8}\times z^{-3}\) - step11: Multiply the terms: \(a^{-12}b^{8}c^{9}y^{9}x^{10}z^{8-3}\) - step12: Subtract the numbers: \(a^{-12}b^{8}c^{9}y^{9}x^{10}z^{5}\) - step13: Simplify: \(\frac{b^{8}c^{9}y^{9}x^{10}z^{5}}{a^{12}}\) Here are the simplified results for each of the expressions: 1. For the expression \[ \frac{\left(x^{2} y^{3} z^{-6}\right)\left(a^{5} x^{4} z^{3}\right)}{\left(a^{2} x^{3} y^{2} z^{6}\right)} \] the simplified result is \[ \frac{x^{3} y a^{3}}{z^{9}}. \] 2. For the expression \[ \frac{\left(a^{-2} b^{5} c^{6} y^{9}\right)\left(a^{-4} b^{3} x^{6} z^{8}\right)}{\left(a^{6} c^{-3} x^{-4} z^{3}\right)} \] the simplified result is \[ \frac{b^{8} c^{9} y^{9} x^{10} z^{5}}{a^{12}}. \] 3. For the expression \[ \frac{\left(x^{6} y^{7} z^{8}\right)\left(x^{3} y^{2} z^{1}\right)\left(a^{6} b^{4}\right)}{\left(a^{2} b^{4} c^{6}\right)\left(x^{1} y^{2} z^{3}\right)\left(x^{8} y^{7}\right)} \] the simplified result is \[ \frac{z^{6} a^{4}}{c^{6}}. \] If you have any further questions or need additional assistance, feel free to ask!