Solution 1.3:4d

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
Current revision (14:10, 22 September 2008) (edit) (undo)
m
 
Line 1: Line 1:
-
The partial expression
+
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>.
-
<math>2^{2^{3}}</math>
+
-
should be interpreted as
+
-
<math>2</math>
+
-
raised to the
+
-
<math>2^{3}</math>,
+
-
and because
+
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
-
<math>2^{3}=2\centerdot 2\centerdot 2=8</math>, thus
+
-
<math>2^{2^{3}}=2^{8}</math>
+
-
 
+
-
 
+
-
In order to calculate the next part of the expression,
+
-
<math>\left( -2 \right)^{-4}</math>,
+
-
 
+
-
it can be useful to do it a step at a time:
+
-
 
+
-
 
+
-
<math>\begin{align}
+
-
& \left( -2 \right)^{-4}=\frac{1}{\left( -2 \right)^{4}}=\frac{1}{\left( \left( -1 \right)\centerdot 2 \right)^{4}}=\frac{1}{\left( -1 \right)^{4}\centerdot 2^{4}} \\
+
-
& \\
+
-
& =\frac{1}{1^{4}\centerdot 2^{4}}=\frac{1}{2^{4}}=2^{-4} \\
+
-
\end{align}</math>
+
 +
{{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,
Thus,
-
 
+
{{Displayed math||<math>2^{2^{3}}\cdot (-2)^{-4} = 2^{8}\cdot 2^{-4} = 2^{8-4} = 2^{4} = 16\,</math>.}}
-
<math>2^{2^{3}}\centerdot \left( -2 \right)^{-4}=2^{8}\centerdot 2^{-4}=2^{8-4}=2^{4}=16</math>
+

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\,.
Retrieved from "http://wiki.sommarmatte.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_1.3:4d"