From Förberedande kurs i matematik 1

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-	{{NAVCONTENT_START}}	+	One way to compare the two numbers is to rewrite the power <math>\bigl(5^{\frac{1}{3}}\bigr)^{4}</math> so that it has the same exponent as <math>400^{\frac{1}{3}}</math>,
-	<center> [[Image:1_3_6d.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\bigl(5^{\frac{1}{3}}\bigr)^{4} = 5^{\frac{1}{3}\cdot 4} = 5^{4\cdot\frac{1}{3}} = \bigl(5^{4}\bigr)^{\frac{1}{3}} = \bigl(5\cdot 5\cdot 5\cdot 5\bigr)^{\frac{1}{3}} = 625^{\frac{1}{3}}\,</math>.}}
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		+	Now, we see that <math>\bigl(5^{\frac{1}{3}}\bigr)^{4} > 400^{\frac{1}{3}}</math>, because <math>625 > 400</math> and the exponent 1/3 is positive.

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Current revision

One way to compare the two numbers is to rewrite the power \displaystyle \bigl(5^{\frac{1}{3}}\bigr)^{4} so that it has the same exponent as \displaystyle 400^{\frac{1}{3}},

\displaystyle \bigl(5^{\frac{1}{3}}\bigr)^{4} = 5^{\frac{1}{3}\cdot 4} = 5^{4\cdot\frac{1}{3}} = \bigl(5^{4}\bigr)^{\frac{1}{3}} = \bigl(5\cdot 5\cdot 5\cdot 5\bigr)^{\frac{1}{3}} = 625^{\frac{1}{3}}\,.

Now, we see that \displaystyle \bigl(5^{\frac{1}{3}}\bigr)^{4} > 400^{\frac{1}{3}}, because \displaystyle 625 > 400 and the exponent 1/3 is positive.