http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?action=history&feed=atom&title=Solution_1.3%3A4c 2026-04-08T15:40:47Z Revision history for this page on the wiki MediaWiki 1.11.1 http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_1.3:4c&diff=5368&oldid=prev 2008-09-22T14:05:19Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 14:05, 22 September 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The whole expression consists of factors having a base of </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The whole expression consists of factors having a base of 5 <ins style="color: red; font-weight: bold; text-decoration: none;">so the power rules can be used to simplify the expression first</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;</del>5<del style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;; </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">so the power rules can be use to </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{{Displayed math||</ins>&lt;math&gt;\begin{align}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">simplify the expression first:</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\frac{5^{12}}{5^{-4}}\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">bigl</ins>( 5^{2} \<ins style="color: red; font-weight: bold; text-decoration: none;">bigr</ins>)^{-6}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= \frac{5^{12}}{5^{-4}}\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>5^{2\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>(-6)}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[3pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= \frac{5^{12}}{5^{-4}}\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>5^{-12}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[3pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\begin{align}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= \frac{5^{12}\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>5^{-12}}{5^{-4}}\\<ins style="color: red; font-weight: bold; text-decoration: none;">[3pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&amp; </del>\frac{5^{12}}{5^{-4}}\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\<del style="color: red; font-weight: bold; text-decoration: none;">left</del>( 5^{2} \<del style="color: red; font-weight: bold; text-decoration: none;">right</del>)^{-6}=\frac{5^{12}}{5^{-4}}\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>5^{2\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot \left</del>( -6 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)}=\frac{5^{12}}{5^{-4}}\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>5^{-12}=\frac{5^{12}\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>5^{-12}}{5^{-4}} \\ </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&amp;= \frac{5^{12-12}}{5^{-4}}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[3pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&amp; \\ </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= \frac{5^{0}}{5^{-4}}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[3pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&amp; =\frac{5^{12-12}}{5^{-4}}=\frac{5^{0}}{5^{-4}}=5^{0-<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( -4 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)}=5^{4}=5\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>5\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>5\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>5=625 \\ </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= 5^{0-(-4)}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[3pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\end{align}&lt;/math&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= 5^{4}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[3pt]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= 5\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>5\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>5\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>5<ins style="color: red; font-weight: bold; text-decoration: none;">\\[3pt]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= 625\<ins style="color: red; font-weight: bold; text-decoration: none;">,</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">textrm{.} </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\end{align}&lt;/math&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">}}</ins></div></td></tr> </table>

Tek http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_1.3:4c&diff=5090&oldid=prev 2008-09-15T11:50:45Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 11:50, 15 September 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">{{NAVCONTENT_START}}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The whole expression consists of factors having a base of </ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;<del style="color: red; font-weight: bold; text-decoration: none;">center</del>&gt; <del style="color: red; font-weight: bold; text-decoration: none;">[[Image:1_3_4c.gif]] </del>&lt;/<del style="color: red; font-weight: bold; text-decoration: none;">center</del>&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">5</ins>&lt;/<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">; </ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_STOP</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">so the power rules can be use to </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">simplify the expression first:</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;\begin</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">align}</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp; \frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">5^{12</ins>}}<ins style="color: red; font-weight: bold; text-decoration: none;">{5^{-4}}\centerdot \left( 5^{2} \right)^{-6}=\frac{5^{12}}{5^{-4}}\centerdot 5^{2\centerdot \left( -6 \right)}=\frac{5^{12}}{5^{-4}}\centerdot 5^{-12}=\frac{5^{12}\centerdot 5^{-12}}{5^{-4}} \\ </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp; \\ </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp; =\frac{5^{12-12}}{5^{-4}}=\frac{5^{0}}{5^{-4}}=5^{0-\left( -4 \right)}=5^{4}=5\centerdot 5\centerdot 5\centerdot 5=625 \\ </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\end{align}&lt;/math&gt;</ins></div></td></tr> </table>

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<p><a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=L%C3%B6sning_1.3:4c&amp;action=edit" class="new" title="Lösning 1.3:4c">Lösning 1.3:4c</a> moved to <a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php/Solution_1.3:4c" title="Solution 1.3:4c">Solution 1.3:4c</a>: Robot: moved page</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 08:25, 9 September 2008</td> </tr> </table>

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<p>Robot: Automated text replacement (-[[Bild: +[[Image:)</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 06:29, 21 August 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;center&gt; [[<del style="color: red; font-weight: bold; text-decoration: none;">Bild</del>:1_3_4c.gif]] &lt;/center&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;center&gt; [[<ins style="color: red; font-weight: bold; text-decoration: none;">Image</ins>:1_3_4c.gif]] &lt;/center&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td></tr> </table>

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