How do you simplify $\sqrt[3]{24 a^{10} b^{6}}$ $root3(24a^10b^6)$ ?

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How do you simplify $\sqrt[3]{24 a^{10} b^{6}}$ $root3(24a^10b^6)$ ?

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Answer 1 · 2016-07-06T10:10:05

$\sqrt[3]{24 a^{10} b^{6}} = 2 a^{3} b^{2} \sqrt[3]{3 a}$ $root(3)(24a^10b^6)=2a^3b^2root(3)(3a)$

Explanation:

$\sqrt[3]{24 a^{10} b^{6}}$ $root(3)(24a^10b^6$

Now $a^{10} = a^{3 + 3 + 3 + 1} = a^{3} \times a^{3} \times a^{3} \times a$ $a^10=a^(3+3+3+1)=a^3xxa^3xxa^3xxa$ and $b^{6} = b^{2 + 2 + 2} = b^{2} \times b^{2} \times b^{2}$ $b^6=b^(2+2+2)=b^2xxb^2 xxb^2$ and such above is equal to
$\sqrt[3]{2 \times 2 \times 2 \times 3 \times a^{3} \times a^{3} \times a^{3} \times a \times b^{2} \times b^{2} \times b^{2}}$ $root(3)(2xx2xx2xx3xxa^3xxa^3xxa^3xxaxxb^2xxb^2 xxb^2$

= $root(3)(ul(2xx2xx2)xx3xx ul(a^3xxa^3xxa^3)xxaxx ul(b^2xxb^2 xxb^2)$

= $2xxa^3xxb^2xxroot(3)(3xxa)$

= $2a^3b^2root(3)3a$

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How do you simplify $\sqrt[3]{24 a^{10} b^{6}}$ $root3(24a^10b^6)$ ?

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How do you simplify root3(24a^10b^6)3√24a10b6root3(24a^10b^6)?

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How do you simplify $\sqrt[3]{24 a^{10} b^{6}}$ $root3(24a^10b^6)$ ?