How do you simplify $root3(4x^2)color(white)(..)root3(8x^7)$ ?

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Answer 1 · 2018-04-12T09:33:22

$2^(5/3)x^3$

$sqrtx$ = $x^(1/2)$

So we can change the question to

$(4x^2)^(1/3)$ $xx$ $(8x^7)^(1/3)$

$4^(1/3)x^(2/3)$ $xx$ $8^(1/3)x^(7/3)$

$4=2^2$ so $4^(1/3)$ = $(2^2)^(1/3)$ = $2^(2/3)$

$8^(1/3)=2$

So the question becomes

$2^(2/3)x^(2/3)$ $xx$ $2x^(7/3)$ = $2^(5/3)x^(9/3)$ = $2^(5/3)x^3$

Answer 2 · 2018-04-12T09:39:41

$2^(5/3)x^3$

Expression $= root3(4x^2)root3(8x^7)$

Remember: $root3(a) xx root3(b) = root3(ab)$

Hence, Expression $=root3(4x^2xx8x^7)$

$= root3(32x^9)$

$= root3(32) xx root3(x^9)$

$= root3(2^5) xx root3(x^9)$

$= 2^(5/3)xx (x^9)^(1/3)$

$= 2^(5/3)x^3$

How do you simplify root3(4x^2)color(white)(..)root3(8x^7)root3(4x^2)color(white)(..)root3(8x^7)?