Question

What values of c and d make the equation true?

Answer 1

c = 6 d = 2

on edge

Answer 2

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

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.