Answer:
the equation is true only if c=6 and d=2.
Step-by-step explanation:
We have the following expression:
[tex]\sqrt[3]{162x^{c}y^{5}} = 3x^{2}y\sqrt[3]{6y^{d}}[/tex]
Elevating to the power of three:
[tex]162x^{c}y^{5}=27x^{6}y^{3}(6y^{d})[/tex]
Simplifying:
→ [tex]162x^{c}y^{5}=162x^{6}y^{3}y^{d}[/tex]
→ [tex]x^{c}y^{5}=x^{6}y^{3}y^{d}[/tex]
→ [tex]x^{c}y^{5}=x^{6}y^{d+3}[/tex]
By comparing the two expression, we can say that:
[tex]c=6[/tex]
[tex]d+3 = 5[/tex] → [tex]d=2[/tex]
Therefore, the equation is true only if c=6 and d=2.
