From Förberedande kurs i matematik 1

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-	{{NAVCONTENT_START}}	+	In order to eliminate <math>\sqrt[3]{7} = 7^{1/3}</math> from the denominator, we can multiply the top and bottom of the fraction by <math>7^{2/3}</math>. The denominator becomes <math>7^{1/3}\cdot 7^{2/3} = 7^{1/3+2/3} = 7^1 = 7</math> and we get
-	<center> [[Image:3_1_5b.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\frac{1}{\sqrt[3]{7}} = \frac{1}{7^{1/3}} = \frac{1}{7^{1/3}}\cdot \frac{7^{2/3}}{7^{2/3}} = \frac{7^{2/3}}{7}\,\textrm{.}</math>}}

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Current revision

In order to eliminate \displaystyle \sqrt[3]{7} = 7^{1/3} from the denominator, we can multiply the top and bottom of the fraction by \displaystyle 7^{2/3}. The denominator becomes \displaystyle 7^{1/3}\cdot 7^{2/3} = 7^{1/3+2/3} = 7^1 = 7 and we get

\displaystyle \frac{1}{\sqrt[3]{7}} = \frac{1}{7^{1/3}} = \frac{1}{7^{1/3}}\cdot \frac{7^{2/3}}{7^{2/3}} = \frac{7^{2/3}}{7}\,\textrm{.}