Question

Which expression is a perfect cube?

-8x^21 y^8
-64x^64 y^64
-125x^9 y^20
-216x^9 y^18

Answer 1

216x^9 y^18 is a perfect cube

Explanation:

To find out the expression that is a perfect cube, we need to take cube root for each expression

`\sqrt[3]{8x^21 y^8} = \sqrt[3]{2^3x^(21) y^8}=2^{(3)/(3)} x^{(21)/(3)} y^{(8)/(3)}`

8 is not divisible by 3 so it is not a perfect cube

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

64 is not divisble by 3

`\sqrt[3]{125x^9 y^20} = \sqrt[3]{5^3x^9 y^(20)}=5^{(3)/(3)} x^{(9)/(3)} y^{(20)/(3)}`

20 is not divisible by 3

`\sqrt[3]{216x^9 y^(18)} = \sqrt[3]{6^3x^9 y^(18)}=6^{(3)/(3)} x^{(9)/(3)} y^{(18)/(3)}=6x^3y^6`

Answer 2

-216x^9 y^18 is a perfect cube