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

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

So, this is not a perfect cube.

The second option is

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

So, this is not a perfect cube.

The third option is

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

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.

Answer 2

Which monomial is a perfect cube?16x627x832x1264x6

Its D