Question

What values of c and d make the equation true?

Answer 1

Answer:

the equation is true only if c=6 and d=2.

Step-by-step explanation:

We have the following expression:

$\sqrt[3]{162x^{c}y^{5}} = 3x^{2}y\sqrt[3]{6y^{d}}$

Elevating to the power of three:

$162x^{c}y^{5}=27x^{6}y^{3}(6y^{d})$

Simplifying:

→ $162x^{c}y^{5}=162x^{6}y^{3}y^{d}$

→ $x^{c}y^{5}=x^{6}y^{3}y^{d}$

→ $x^{c}y^{5}=x^{6}y^{d+3}$

By comparing the two expression, we can say that:

$c=6$

$d+3 = 5$ → $d=2$

Therefore, the equation is true only if c=6 and d=2.