How do you write $a^{1.5}$ $a^1.5$ in radical form?

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How do you write $a^{1.5}$ $a^1.5$ in radical form?

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Answer 1 · 2017-01-08T15:51:28

See full explanation below:

Explanation:

Because $1.5 = \frac{3}{2}$ $1.5 = 3/2$ we can rewrite this expression as:

$a^{\frac{3}{2}}$ $a^(3/2)$

We can now use this rule for exponents to modify the expression:

${(x^{a})}^{b} = x^{a \times b}$ $(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))$ and $x^{a \times b} = {(x^{a})}^{b}$ $x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)$

$a^{\frac{3}{2}} \to a^{3 \times \frac{1}{2}} \to {(a^{3})}^{\frac{1}{2}}$ $a^(color(red)(3)/color(blue)(2)) -> a^(color(red)(3) xx 1/color(blue)(2)) -> (a^(color(red)(3)))^(1/color(blue)(2))$

Now we can use this rule to put this in a radical form:

$x^{\frac{1}{n}} = \sqrt[n]{x}$ $x^(1/color(red)(n)) = root(color(red)(n))(x)$

${(a^{3})}^{\frac{1}{2}} \to \sqrt[2]{a^{3}} \to \sqrt{a^{3}}$ $(a^(color(red)(3)))^(1/color(blue)(2)) -> root(color(blue)(2))(a^(color(red)(3))) -> sqrt(a^(color(red)(3)))$

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How do you write $a^{1.5}$ $a^1.5$ in radical form?

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Explanation:

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How do you write a1.5a^1.5 in radical form?

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How do you write $a^{1.5}$ $a^1.5$ in radical form?