Question

Which expression is a perfect cube?

Answer 1

Answer:

216x^9 y^18 is a perfect cube

Step-by-step explanation:

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

$\sqrt[3]{8x^21 y^8} = \sqrt[3]{2^3x^{21} y^8}=2^{\frac{3}{3}} x^{\frac{21}{3}} y^{\frac{8}{3}}$

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

$\sqrt[3]{64x^64 y^64} = \sqrt[3]{2^6x^{64} y^{64}}=2^{\frac{6}{3}} x^{\frac{64}{3}} y^{\frac{64}{3}}$

64 is not divisble by 3

$\sqrt[3]{125x^9 y^20} = \sqrt[3]{5^3x^9 y^{20}}=5^{\frac{3}{3}} x^{\frac{9}{3}} y^{\frac{20}{3}}$

20 is not divisible by 3

$\sqrt[3]{216x^9 y^{18}} = \sqrt[3]{6^3x^9 y^{18}}=6^{\frac{3}{3}} x^{\frac{9}{3}} y^{\frac{18}{3}}=6x^3y^6$

Answer 2

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