How do you write $5 x^{\frac{5}{2}}$ $5x^(5/2)$ as a radical form?

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How do you write $5 x^{\frac{5}{2}}$ $5x^(5/2)$ as a radical form?

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Answer 1 · 2016-04-23T15:36:44

$5 \sqrt{x^{5}}$ $5sqrt(x^5)$ or $5 x^{2} \sqrt{x}$ $5x^2sqrt(x)$

Explanation:

If $x \geq 0$ $x >= 0$ then:

$5 x^{\frac{5}{2}} = 5 x^{5 \cdot \frac{1}{2}} = 5 {(x^{5})}^{\frac{1}{2}} = 5 \sqrt{x^{5}}$ $5x^(5/2) = 5x^(5*1/2) = 5(x^5)^(1/2) = 5sqrt(x^5)$

If you prefer:

$5 x^{\frac{5}{2}} = 5 x^{2 + \frac{1}{2}} = 5 x^{2} x^{\frac{1}{2}} = 5 x^{2} \sqrt{x}$ $5x^(5/2) = 5x^(2+1/2) = 5x^2x^(1/2) = 5x^2sqrt(x)$

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Footnote

Fractional exponents like this tend to work well with non-negative numbers, but can misbehave horribly for negative or Complex numbers.

For example:

${(- 1)}^{\frac{3}{2}} = - i \neq i = {({(- 1)}^{3})}^{\frac{1}{2}}$ $(-1)^(3/2) = -i != i = ((-1)^3)^(1/2)$

or even:

${({(- 1)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(- i)}^{\frac{2}{3}} = \frac{1}{2} - \frac{\sqrt{3}}{2} i \neq - 1 = {(- 1)}^{\frac{3}{2} \cdot \frac{2}{3}}$ $((-1)^(3/2))^(2/3) = (-i)^(2/3) = 1/2-sqrt(3)/2i != -1 = (-1)^(3/2 * 2/3)$

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How do you write $5 x^{\frac{5}{2}}$ $5x^(5/2)$ as a radical form?

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How do you write $5 x^{\frac{5}{2}}$ $5x^(5/2)$ as a radical form?