j) $$ \frac{\left(x y z^{2} ight)^{-1}}{x^{2} y^{-1} z^{3}} \div\left(\frac{x^{3} y^{2} z^{0}}{x^{4} y^{2} z^{-3}} ight)^{-1} imes \frac{x y^{2} z^{4}}{x^{-3} y^{2} z^{0}} $$

Question

j) $$ \frac{\left(x y z^{2}ight)^{-1}}{x^{2} y^{-1} z^{3}} \div\left(\frac{x^{3} y^{2} z^{0}}{x^{4} y^{2} z^{-3}}ight)^{-1} 	imes \frac{x y^{2} z^{4}}{x^{-3} y^{2} z^{0}} $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ (x*y*z^2)^{-1}/(x^2*y^{-1}*z^3) \div ((x^3*y^2*z^0)/(x^4*y^2*z^{-3}))^{-1} 	imes (x*y^2*z^4)/(x^{-3}*y^2*z^0) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\frac{\left(xyz^{2}ight)^{-1}}{\left(x^{2}y^{-1}z^{3}ight)}\div \left(\frac{\left(x^{3}y^{2}z^{0}ight)}{\left(x^{4}y^{2}z^{-3}ight)}ight)^{-1}\left(xy^{2}z^{4}ight)}{\left(x^{-3}y^{2}z^{0}ight)}$$
- step1: Evaluate:
  $$\frac{\frac{\left(xyz^{2}ight)^{-1}}{\left(x^{2}y^{-1}z^{3}ight)}\div \left(\frac{\left(x^{3}y^{2}z^{0}ight)}{\left(x^{4}y^{2}z^{-3}ight)}ight)^{-1}xy^{2}z^{4}}{\left(x^{-3}y^{2}z^{0}ight)}$$
- step2: Remove the parentheses:
  $$\frac{\frac{\left(xyz^{2}ight)^{-1}}{x^{2}y^{-1}z^{3}}\div \left(\frac{x^{3}y^{2}z^{0}}{x^{4}y^{2}z^{-3}}ight)^{-1}xy^{2}z^{4}}{x^{-3}y^{2}z^{0}}$$
- step3: Multiply by $$a^{-n}:$$
  $$\frac{\frac{\left(xyz^{2}ight)^{-1}}{x^{2}y^{-1}z^{3}}\div \left(x^{3}y^{2}z^{0}x^{-4}y^{-2}z^{3}ight)^{-1}xy^{2}z^{4}}{x^{-3}y^{2}z^{0}}$$
- step4: Evaluate the power:
  $$\frac{\frac{\left(xyz^{2}ight)^{-1}}{x^{2}y^{-1}z^{3}}\div \left(x^{3}y^{2}	imes 1	imes x^{-4}y^{-2}z^{3}ight)^{-1}xy^{2}z^{4}}{x^{-3}y^{2}z^{0}}$$
- step5: Multiply the terms:
  $$\frac{\frac{\left(xyz^{2}ight)^{-1}}{x^{2}y^{-1}z^{3}}\div \left(x^{-1}z^{3}ight)^{-1}xy^{2}z^{4}}{x^{-3}y^{2}z^{0}}$$
- step6: Divide the terms:
  $$\frac{\frac{1}{x^{3}z^{5}}\div \left(x^{-1}z^{3}ight)^{-1}xy^{2}z^{4}}{x^{-3}y^{2}z^{0}}$$
- step7: Divide the terms:
  $$\frac{\frac{1}{x^{4}z^{2}}	imes xy^{2}z^{4}}{x^{-3}y^{2}z^{0}}$$
- step8: Evaluate the power:
  $$\frac{\frac{1}{x^{4}z^{2}}	imes xy^{2}z^{4}}{x^{-3}y^{2}	imes 1}$$
- step9: Calculate:
  $$\frac{\frac{1}{x^{4}z^{2}}	imes xy^{2}z^{4}}{x^{-3}y^{2}}$$
- step10: Reduce the fraction:
  $$\frac{1}{x^{4}z^{2}}	imes x^{4}z^{4}$$
- step11: Multiply the terms:
  $$\frac{1}{z^{2}}	imes z^{4}$$
- step12: Reduce the fraction:
  $$1	imes z^{2}$$
- step13: Multiply the terms:
  $$z^{2}$$
The simplified expression is $$ z^{2} $$.
The simplified expression is $$ z^{2} $$.

j) \( \frac{\left(x y z^{2}\right)^{-1}}{x^{2} y^{-1} z^{3}} \div\left(\frac{x^{3} y^{2} z^{0}}{x^{4} y^{2} z^{-3}}\right)^{-1} \times \frac{x y^{2} z^{4}}{x^{-3} y^{2} z^{0}} \)

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