Answer:
c=1 and c=3
Step-by-step explanation:
If x>0 and y>0, then
\sqrt{\dfrac{50x^6y^3}{9x^8}}=\sqrt{\dfrac{25\cdot 2y^2\cdot y}{9x^2}}=\dfrac{5y\sqrt{2y}}{3x}.
9x
8
50x
6
y
3
=
9x
2
25⋅2y
2
⋅y
=
3x
5y
2y
.
If
\dfrac{5y\sqrt{2y}}{3x}
3x
5y
2y
is equal to
\dfrac{5y^c\sqrt{2y}}{dx},
dx
5y
c
2y
,
then
\begin{gathered}y=y^c\Rightarrow c=1,\\ \\3x=dx\Rightarrow d=3.\end{gathered}
y=y
c
⇒c=1,
3x=dx⇒d=3.
