$root(3)(20x^2y^7)*root(3)(50x^4y^2)$ = ?

Question

A) $20^(1/3)(50^(1/3))x^(6)y^9$
B) $70^(1/3)x^(2)y^3$

C) $10x^(8/3)y^(14/3)$
D) $10x^2y^3$
E) $1000x^(8/3)y^(14/3)$

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Answer 1 · 2018-06-01T21:58:24

d) $10x^2y^3$

$=root(3)(20x^2y^7)*root(3)(50x^4y^2)$

$=root(3)((20x^2y^7)*(50x^4y^2))$

$=root3(1000x^6y^9)$

$=root3(10^3x^6y^9)$

$=10x^2y^3$