The values of c and d which makes the provided equation of variable x and y true is 1 and 3 respectively.
Unknown variables are used to find the unknown values of the problem using the algebraic expressions.
The variable x is greater-than 0. Thus,
[tex]x > 0[/tex]
The variable y greater-than-or-equal-to zero. Thus,
[tex]y\geq0[/tex]
The given expression is attached in the image below, which is,
[tex]\sqrt{\dfrac{50x^6y^3}{9x^6}}={\dfrac{5y^c\sqrt{2y}}{dx}}[/tex]
Cancel out x⁶ term and solve it further with
[tex]\sqrt{\dfrac{(25\times2)x^6(y^2\times y)}{(3^2)(x^6\times x^2)}}={\dfrac{5y^c\sqrt{2y}}{dx}}\\\sqrt{\dfrac{(5^2\times2)(y^2\times y)}{(3^2)(x^2)}}={\dfrac{5y^c\sqrt{2y}}{dx}}\\{\dfrac{(5y)\sqrt{(2y)}}{(3x)}}={\dfrac{5y^c\sqrt{2y}}{dx}}[/tex]
Compare both the equation, we get,
[tex]5y=5y^c\\1=c[/tex]
[tex]3x=dx\\3=d[/tex]
Thus, the values of c and d which makes the provided equation of variable x and y true is 1 and 3 respectively.
Learn more about the unknown variable here;
https://brainly.com/question/1235185
