How do you simplify $\sqrt[3]{4 x^{2}} . . \sqrt[3]{8 x^{7}}$ $root3(4x^2)color(white)(..)root3(8x^7)$ ?

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How do you simplify $\sqrt[3]{4 x^{2}} . . \sqrt[3]{8 x^{7}}$ $root3(4x^2)color(white)(..)root3(8x^7)$ ?

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Answer 1 · 2018-04-12T09:33:22

$2^{\frac{5}{3}} x^{3}$ $2^(5/3)x^3$

Explanation:

$\sqrt{x}$ $sqrtx$ = $x^{\frac{1}{2}}$ $x^(1/2)$

So we can change the question to

${(4 x^{2})}^{\frac{1}{3}}$ $(4x^2)^(1/3)$ $\times$ $xx$ ${(8 x^{7})}^{\frac{1}{3}}$ $(8x^7)^(1/3)$

$4^{\frac{1}{3}} x^{\frac{2}{3}}$ $4^(1/3)x^(2/3)$ $\times$ $xx$ $8^{\frac{1}{3}} x^{\frac{7}{3}}$ $8^(1/3)x^(7/3)$

$4 = 2^{2}$ $4=2^2$ so $4^{\frac{1}{3}}$ $4^(1/3)$ = ${(2^{2})}^{\frac{1}{3}}$ $(2^2)^(1/3)$ = $2^{\frac{2}{3}}$ $2^(2/3)$

$8^{\frac{1}{3}} = 2$ $8^(1/3)=2$

So the question becomes

$2^{\frac{2}{3}} x^{\frac{2}{3}}$ $2^(2/3)x^(2/3)$ $\times$ $xx$ $2 x^{\frac{7}{3}}$ $2x^(7/3)$ = $2^{\frac{5}{3}} x^{\frac{9}{3}}$ $2^(5/3)x^(9/3)$ = $2^{\frac{5}{3}} x^{3}$ $2^(5/3)x^3$

Answer 2 · 2018-04-12T09:39:41

$2^{\frac{5}{3}} x^{3}$ $2^(5/3)x^3$

Explanation:

Expression $= \sqrt[3]{4 x^{2}} \sqrt[3]{8 x^{7}}$ $= root3(4x^2)root3(8x^7)$

Remember: $\sqrt[3]{a} \times \sqrt[3]{b} = \sqrt[3]{a b}$ $root3(a) xx root3(b) = root3(ab)$

Hence, Expression $= \sqrt[3]{4 x^{2} \times 8 x^{7}}$ $=root3(4x^2xx8x^7)$

$= \sqrt[3]{32 x^{9}}$ $= root3(32x^9)$

$= \sqrt[3]{32} \times \sqrt[3]{x^{9}}$ $= root3(32) xx root3(x^9)$

$= \sqrt[3]{2^{5}} \times \sqrt[3]{x^{9}}$ $= root3(2^5) xx root3(x^9)$

$= 2^{\frac{5}{3}} \times {(x^{9})}^{\frac{1}{3}}$ $= 2^(5/3)xx (x^9)^(1/3)$

$= 2^{\frac{5}{3}} x^{3}$ $= 2^(5/3)x^3$

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How do you simplify $\sqrt[3]{4 x^{2}} . . \sqrt[3]{8 x^{7}}$ $root3(4x^2)color(white)(..)root3(8x^7)$ ?

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