From Förberedande kurs i matematik 1

Revision as of 08:25, 9 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 1.3:4d moved to Solution 1.3:4d: Robot: moved page) ← Previous diff		Current revision (14:10, 22 September 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	The partial expression <math>2^{2^{3}}</math> should be interpreted as 2 raised to the <math>2^{3}</math>, and because <math>2^{3}=2\cdot 2\cdot 2=8</math>, thus <math>2^{2^{3}}=2^{8}</math>.
-	<center> [[Image:1_3_4d.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	In order to calculate the next part of the expression, <math>(-2)^{-4}</math>, it can be useful to do it a step at a time
		+
		+	{{Displayed math||<math>\begin{align}
		+	(-2)^{-4} &= \frac{1}{(-2)^{4}} = \frac{1}{((-1)\cdot 2)^{4}} = \frac{1}{(-1)^{4}\cdot 2^{4}}\\[5pt]
		+	&= \frac{1}{1\cdot 2^{4}} = \frac{1}{2^{4}} = 2^{-4}\,\textrm{.}
		+	\end{align}</math>}}
		+
		+	Thus,
		+
		+	{{Displayed math||<math>2^{2^{3}}\cdot (-2)^{-4} = 2^{8}\cdot 2^{-4} = 2^{8-4} = 2^{4} = 16\,</math>.}}

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Current revision

The partial expression \displaystyle 2^{2^{3}} should be interpreted as 2 raised to the \displaystyle 2^{3}, and because \displaystyle 2^{3}=2\cdot 2\cdot 2=8, thus \displaystyle 2^{2^{3}}=2^{8}.

In order to calculate the next part of the expression, \displaystyle (-2)^{-4}, it can be useful to do it a step at a time

\displaystyle \begin{align} (-2)^{-4} &= \frac{1}{(-2)^{4}} = \frac{1}{((-1)\cdot 2)^{4}} = \frac{1}{(-1)^{4}\cdot 2^{4}}\\[5pt] &= \frac{1}{1\cdot 2^{4}} = \frac{1}{2^{4}} = 2^{-4}\,\textrm{.} \end{align}

Thus,

\displaystyle 2^{2^{3}}\cdot (-2)^{-4} = 2^{8}\cdot 2^{-4} = 2^{8-4} = 2^{4} = 16\,.