Answer to Question #125278 in Algebra for EMMANUEL

Question

Simplify. X^p+(1/2)q ×Y^2p-q ÷ (XY^2)^P × √X^q

Answer 1

I assume your question is: $x^{p+\frac q 2}\times y^{2p-q} \div (xy^2)^p \times (\sqrt {x})^q$

Then the solution is:

$x^{p+\frac q 2}\times y^{2p-q} \div (xy^2)^p \times (\sqrt {x})^q =$ $x^{p+\frac q 2}\times y^{2p-q} \times \frac {x^{q/2}}{(xy^2)^p} =$

$=x^{p+\frac q 2+\frac q 2 -p}\times y^{2p-q-2p} =x^q \times y^{-q} = (\frac x y)^q$

Final answer: $(\frac x y)^q$