x-2-p-and-y-2-q-Evaluate-in-terms-of-x-and-or-y-i-2-p-q-ii-2-2q-iii-2-p-1-

Question Number 137634 by mey3nipaba last updated on 04/Apr/21

$${x}=\mathrm{2}^{{p}\:} {and}\:{y}=\mathrm{2}^{{q}\:} .\:{Evaluate}\:{in}\:{terms}\:{of}\:{x}\:{and}/\:{or}\:{y}\: \\ $$$$\left({i}\right)\mathrm{2}^{{p}+{q}} \:\:\left({ii}\right)\:\mathrm{2}^{\mathrm{2}{q}\:} \:\:\:\left({iii}\right)\:\mathrm{2}^{{p}−\mathrm{1}} \\ $$

Answered by mr W last updated on 04/Apr/21

2^(p+q) =2^p 2^q =xy 2^(2q) =(2^q )^2 =y^2 2^(p−1) =(2^p /2)=(x/2)

$$\mathrm{2}^{{p}+{q}} =\mathrm{2}^{{p}} \mathrm{2}^{{q}} ={xy} \\ $$$$\mathrm{2}^{\mathrm{2}{q}} =\left(\mathrm{2}^{{q}} \right)^{\mathrm{2}} ={y}^{\mathrm{2}} \\ $$$$\mathrm{2}^{{p}−\mathrm{1}} =\frac{\mathrm{2}^{{p}} }{\mathrm{2}}=\frac{{x}}{\mathrm{2}} \\ $$

Commented by mey3nipaba last updated on 05/Apr/21

$${Thank}\:{you}\:{o}\:{much}.\:{I}\:{appreciate}.\:{God}\:{bless}\:{you}. \\ $$

Commented by otchereabdullai@gmail.com last updated on 05/Apr/21

$$\mathrm{well}\:\mathrm{understood} \\ $$

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