Question

Which monomial is a perfect cube?

16x6
27x8
32x12
64x6

Answer 1

Answer: The answer is (D)
`64x^6.`

Step-by-step explanation: We are to select the correct monomial from the given options which is a perfect cube.

The first option is

`y=16x^6=2* (8x^6)=2*(2x^2)^3\\\\\Rightarrow \sqrt[3]{y}=2x^2\sqrt[3]{2}.`

So, this is not a perfect cube.

The second option is

`y=27x^8=x^2* (27x^6)=x^2*(3x^2)^3\\\\\Rightarrow \sqrt[3]{y}=3x^2\sqrt[3]{x^2}.`

So, this is not a perfect cube.

The third option is

`y=32x^(12)=4* (8x^(12))=4*(2x^4)^3\\\\\Rightarrow \sqrt[3]{y}=2x^4\sqrt[3]{4}.`

So, this is not a perfect cube.

The fourth option is

`y=64x^6=(4x^2)^3\\\\\Rightarrow \sqrt[3]{y}=4x^2.`

So, this is a perfect cube.

Thus, (D)
`64x^6` is the correct option.