Which expression is a perfect cube? A. -8x21y8B. -64x64y64C. -125x9y20D. -216x9y18

Finding the cube root of each expression

Expression A:

[tex] \sqrt[3]{-8x^{21}y^{8}} [/tex]
[tex] \sqrt[3]{-8} [/tex] [tex] \sqrt[3]{x^{21}[tex] \sqrt[3]{y^8} [/tex]} [/tex] 
[tex]-2x^ \frac{21}{3} y^ \frac{8}{3} [/tex]
[tex]-2 x^7 y^ \frac{8}{3} [/tex]

the term [tex]y^ \frac{8}{3} [/tex] is not a perfect cube, therefore expression A is not a perfect cube.

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Expression B
[tex] \sqrt[3]{-64x^{64}y^{64}} [/tex]
[tex] \sqrt[3]{-64} \sqrt[3]{x^{64}} \sqrt[3]{y^{64}} [/tex]
[tex]-4 x^ \frac{64}{3} y^ \frac{64}{3} [/tex]

The term [tex]x^ \frac{64}{3} [/tex] and [tex]y^ \frac{64}{3} [/tex] are not perfect cube because 64/3 doesn't give whole number
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Expression C

[tex] \sqrt[3] {-125x^9y^{20}} [/tex]
[tex] \sqrt[3]{-125} \sqrt[3]{x^9} \sqrt[3] {y^{20}} [/tex]
[tex]-5 (x^ \frac{9}{3}) (y^ \frac{20}{3})[/tex]
[tex]-5 (x^3) (y^ \frac{20} {3}) [/tex]

The term [tex]y^ \frac{20}{3} [/tex] are not perfect cube because 20/3 doesn't give whole number
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Expression D

[tex] \sqrt[3]{ -216 x^{9} y^{18} } [/tex]
[tex] \sqrt[3]{-216} \sqrt[3]{x^9} \sqrt[3]{y^{18}} [/tex]
[tex]-6 ( x^ \frac{9} {3} ) ( y^ \frac{18} {3} ) [/tex]
[tex]-6 (x^3) (y^6)[/tex]

All terms are perfect cubes

ANSWER: OPTION D