How do you simplify ${(x^{6})}^{\frac{1}{2}}$ $(x^6)^(1/2)$ ?

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How do you simplify ${(x^{6})}^{\frac{1}{2}}$ $(x^6)^(1/2)$ ?

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Answer 1 · 2017-02-16T22:44:27

$x^{3}$ $x^3$

Explanation:

${(x^{6})}^{\frac{1}{2}}$ $(x^6)^(1/2)$ may also be written as $x^{6 \times \frac{1}{2}} = x^{\frac{6}{2}} = x^{3}$ $" "x^(6xx1/2) = x^(6/2) = x^3$

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By the way ${(x^{6})}^{\frac{1}{2}}$ $(x^6)^(1/2)$ is another way of writing $\sqrt{x^{6}}$ $sqrt(x^6)$

Answer 2 · 2017-02-16T23:58:07

${(x^{6})}^{\frac{1}{2}} = ∣ ∣ x^{3} ∣ ∣$ $(x^6)^(1/2) = abs(x^3)$

Explanation:

Note that if $t \geq 0$ $t >= 0$ then $\sqrt{t^{2}} = t$ $sqrt(t^2) = t$

If $t < 0$ $t < 0$ then $\sqrt{t^{2}} = - t$ $sqrt(t^2) = -t$

To cover both these cases we can write:

$\sqrt{t^{2}} = | t |$ $sqrt(t^2) = abs(t)$

Putting $t = x^{3}$ $t = x^3$ we find:

${(x^{6})}^{\frac{1}{2}} = \sqrt{x^{6}} = \sqrt{{(x^{3})}^{2}} = ∣ ∣ x^{3} ∣ ∣$ $(x^6)^(1/2) = sqrt(x^6) = sqrt((x^3)^2) = abs(x^3)$

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