Question

What values of c and d make the equation true?

Answer 1

Third option.

Step-by-step explanation:

You need to cube both sides of the equation. Remember the Power of a power property:

`(a^m)^n=a^{mn`

`\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d`

According to the Product of powers property:

`(a^m)(a^n)=a^{(m+n)`

Then. simplifying you get:

`162x^cy^5=162x^6y^((3+d))`

Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6, then the exponent of "x" on the left side must be 6. Therefore:

`c=6`

You can notice that the exponent of "y" on the left side is 5, then the exponent of "x" on the left side must be 5 too. Therefore "d" is:

`3+d=5\\d=5-3\\d=2`