Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 152323 by mathdanisur last updated on 27/Aug/21

x^2 ∙y=(1/(18))  and  x∙y^2 =(1/(12))  find  (xy)^(−2)  = ?

$$\mathrm{x}^{\mathrm{2}} \centerdot\mathrm{y}=\frac{\mathrm{1}}{\mathrm{18}}\:\:\mathrm{and}\:\:\mathrm{x}\centerdot\mathrm{y}^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\mathrm{find}\:\:\left(\mathrm{xy}\right)^{−\mathrm{2}} \:=\:? \\ $$

Answered by Olaf_Thorendsen last updated on 27/Aug/21

x^2 y = (1/(18)) and xy^2  = (1/(12))  ⇒ (x^2 y)(xy^2 ) = (xy)^3  = (1/(12×18)) = (1/(216))  xy = (1/( ((216))^(1/3) )) = (1/6)  (xy)^(−2)  = 6^2  = 36

$${x}^{\mathrm{2}} {y}\:=\:\frac{\mathrm{1}}{\mathrm{18}}\:\mathrm{and}\:{xy}^{\mathrm{2}} \:=\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\Rightarrow\:\left({x}^{\mathrm{2}} {y}\right)\left({xy}^{\mathrm{2}} \right)\:=\:\left({xy}\right)^{\mathrm{3}} \:=\:\frac{\mathrm{1}}{\mathrm{12}×\mathrm{18}}\:=\:\frac{\mathrm{1}}{\mathrm{216}} \\ $$$${xy}\:=\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{216}}}\:=\:\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\left({xy}\right)^{−\mathrm{2}} \:=\:\mathrm{6}^{\mathrm{2}} \:=\:\mathrm{36} \\ $$

Commented by mathdanisur last updated on 27/Aug/21

Thank You Ser

$$\mathrm{Thank}\:\mathrm{You}\:\mathrm{Ser} \\ $$

Commented by otchereabdullai@gmail.com last updated on 27/Aug/21

nice one!

$$\mathrm{nice}\:\mathrm{one}! \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com