Question

Which expression is a perfect cube?

A. -8x21y8

B. -64x64y64

C. -125x9y20

D. -216x9y18

Answer 1

Finding the cube root of each expression

Expression A:


`\sqrt[3]{-8x^(21)y^(8)}`

`\sqrt[3]{-8}`
} [/tex]

`-2x^ (21)/(3) y^ (8)/(3)`

`-2 x^7 y^ (8)/(3)`

the term
`y^ (8)/(3)` is not a perfect cube, therefore expression A is not a perfect cube.

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Expression B

`\sqrt[3]{-64x^(64)y^(64)}`

`\sqrt[3]{-64} \sqrt[3]{x^(64)} \sqrt[3]{y^(64)}`

`-4 x^ (64)/(3) y^ (64)/(3)`

The term
`x^ (64)/(3)` and
`y^ (64)/(3)` are not perfect cube because 64/3 doesn't give whole number
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Expression C


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

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

`-5 (x^ (9)/(3)) (y^ (20)/(3))`

`-5 (x^3) (y^ \frac{20} {3})`

The term
`y^ (20)/(3)` are not perfect cube because 20/3 doesn't give whole number
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Expression D


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

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

`-6 ( x^ \frac{9} {3} ) ( y^ \frac{18} {3} )`

`-6 (x^3) (y^6)`

All terms are perfect cubes

ANSWER: OPTION D