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Question Number 185414 by Safiullah_21 last updated on 21/Jan/23

2^x =a  3^y =b      : 6^(xy) =?  ⇒6^(xy) =(2×3)^(xy) ⇒2^(xy) ×3^(xy) ⇒(2^x )^y ×(3^y )^x ⇒a^y ×b^x

$$\mathrm{2}^{{x}} ={a} \\ $$$$\mathrm{3}^{{y}} ={b}\:\:\:\:\:\::\:\mathrm{6}^{{xy}} =? \\ $$$$\Rightarrow\mathrm{6}^{{xy}} =\left(\mathrm{2}×\mathrm{3}\right)^{{xy}} \Rightarrow\mathrm{2}^{{xy}} ×\mathrm{3}^{{xy}} \Rightarrow\left(\mathrm{2}^{{x}} \right)^{{y}} ×\left(\mathrm{3}^{{y}} \right)^{{x}} \Rightarrow{a}^{{y}} ×{b}^{{x}} \\ $$

Commented by mr W last updated on 21/Jan/23

is a^y b^x  better than 6^(xy)  ?

$${is}\:{a}^{{y}} {b}^{{x}} \:{better}\:{than}\:\mathrm{6}^{{xy}} \:? \\ $$

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