How do you simplify ${\sqrt{x}}^{3} \times \sqrt[3]{x^{2}}$ $sqrtx^3 timesroot3(x^2)$ and write it in exponential form?

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How do you simplify ${\sqrt{x}}^{3} \times \sqrt[3]{x^{2}}$ $sqrtx^3 timesroot3(x^2)$ and write it in exponential form?

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Answer 1 · 2016-05-01T20:28:28

$x^{\frac{13}{6}}$ $x^(13/6)$ assuming $x \geq 0$ $x >= 0$

Explanation:

If $x \geq 0$ $x >= 0$ then ${(x^{a})}^{b} = x^{a b}$ $(x^a)^b = x^(ab)$

and $x^{a} \times x^{b} = x^{a + b}$ $x^a xx x^b = x^(a+b)$

Another way of writing $\sqrt[n]{x}$ $root(n)(x)$ is $x^{\frac{1}{n}}$ $x^(1/n)$

So:

${\sqrt{x}}^{3} \times \sqrt[3]{x^{2}}$ $sqrt(x)^3 xx root(3)(x^2)$

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

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

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

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

$= x^{\frac{9}{6} + \frac{4}{6}}$ $=x^(9/6+4/6)$

$= x^{\frac{13}{6}}$ $=x^(13/6)$

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How do you simplify ${\sqrt{x}}^{3} \times \sqrt[3]{x^{2}}$ $sqrtx^3 timesroot3(x^2)$ and write it in exponential form?

1 Answer

Explanation:

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How do you simplify ${\sqrt{x}}^{3} \times \sqrt[3]{x^{2}}$ $sqrtx^3 timesroot3(x^2)$ and write it in exponential form?