<table width=100%><tr><td valign=top><center>\reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width="20" height="20">}</center><div class="toc">\link{main}


<font size=-1>
      \link{mainS1}{}</font>

<div class="selection"><font size=-1>
      \link{mainS2}{}</font></div>

<font size=-1>
      \link{mainS3}{}</font>
</div></td><td valign=top halign=center><div class="wimsdoc"> 

<h2 class="thm">Thorme</h2><div class="thm"> Si \( m \) et \( n \) sont des entiers relatifs, alors&nbsp;:
     <div class="math">\(\begin{matrix} 
    10^m \times 10^n & = & 10^{m+n} \\
     10^{-n} & = & \frac{1}{10^n} \\
     \frac{10^m}{10^n} & = & 10^{m-n} \\
    \left( 10^m \right)^n & = & 10^{m \times n}
    \end{matrix})</div> 
    </div>






	\def{integer a1=10}
	\def{integer m1=random(2..5)*randint(-1,1)}
	\def{integer n1=random(2..5)*randint(-1,1)}
	\def{integer mn1=pari((\m1)+(\n1))}
	\def{integer a2=10}
	\def{integer m2= random(2..5)*randint(-1,1)}
	\def{integer n2=random(2..5)*randint(-1,1)}
	\def{integer mn2=pari((\m2)-(\n2))}
	\def{integer a3=10}
	\def{integer m3= random(2..4)*randint(-1,1)}
	\def{integer n3=random(2..4)*randint(-1,1)}
    \def{integer mn3=pari((\m3)*(\n3))}
	\def{rational result1 = pari( (\a1)^(\m1+\n1))}
	\def{rational result2 = pari( (\a2)^(\m2-\n2))}
	\def{rational result3 = pari( (\a3)^(\m3*\n3))}

\def<table align=center>
<tr><td> A  </td>
  	<td> = </td>
  	<td>\if{\a1<0}{\( (\a1)^{\m1} \times (\a1)^{\n1} )}{\(\a1^{\m1} \times \a1^{\n1})}</td>
	<td> &nbsp; &nbsp; &nbsp; </td>
	<td> B  </td>
  	<td> = </td>
  	<td>\if{\a2<0}{\(\frac{ (\a2)^{\m2}}{ (\a2)^{\n2} })}{\(\frac{\a2^{\m2}}{ \a2^{\n2}})}</td>
	<td> &nbsp; &nbsp; &nbsp; </td>
	<td> C  </td>
  	<td> = </td>
  	<td>\if{\a3<0}{\( \left( (\a3)^{\m3}\right)^{\n3})}{\( \left(\a3^{\m3}\right)^{\n3})}</td>
</tr>

<tr><td> A   </td>
  	<td> = </td>
  	<td>\if{\a1<0}{\( (\a1)^{\m1+(\n1)} )}{\(\a1^{\m1+(\n1)})}</td>
	<td> &nbsp; &nbsp; &nbsp; </td>
	<td> B   </td>
  	<td> = </td>
  	<td>\if{\a2<0}{\( (\a2)^{\m2-(\n2)} )}{\(\a2^{\m2-(\n2)})}</td>
	<td> &nbsp; &nbsp; &nbsp; </td>
	<td> C   </td>
  	<td> = </td>
  	<td>\if{\a3<0}{\( (\a3)^{\m3*(\n3)}) }{\( \a3^{\m3*(\n3)} )}</td>
</tr>

<tr><td> A   </td>
  	<td> = </td>
  	<td>\if{\a1<0}{\( (\a1)^{\mn1} )}{\(\a1^{\mn1})}</td>
	<td> &nbsp; &nbsp; &nbsp; </td>
	<td> B   </td>
  	<td> = </td>
  	<td>\if{\a2<0}{\( (\a2)^{\mn2} )}{\(\a2^{\mn2})}</td>
	<td> &nbsp; &nbsp; &nbsp; </td>
	<td> C   </td>
  	<td> = </td>
  	<td>\if{\a3<0}{\( (\a3)^{\mn3}) }{\( \a3^{\mn3} )}</td>
</tr>

<tr><td> (A   </td>
  	<td> = </td>
  	<td>\( \result1 ))</td>
	<td> &nbsp; &nbsp; &nbsp; </td>
	<td>( B   </td>
  	<td> = </td>
  	<td>\( \result2 ))</td>
	<td> &nbsp; &nbsp; &nbsp; </td>
	<td>( C   </td>
  	<td> = </td>
  	<td>\( \result3 ))</td>
</tr>
</table>





<h2 class="thm">Exercice</h2><div class="thm">
<ul>
<li>\exercise{module=H3/algebra/oefpuis.fr&cmd=new&exo=produit10&cmd=new}{Premire formule}  </li>
<li>\exercise{module=H3/algebra/oefpuis.fr&cmd=new&exo=inverse10 &cmd=new}{Deuxime formule}  </li>
<li>\exercise{module=H3/algebra/oefpuis.fr&cmd=new&exo=quotient10&cmd=new}{Troisime formule}  </li>
<li>\exercise{module=H3/algebra/oefpuis.fr&cmd=new&exo=puispuis10&cmd=new}{Quatrime formule}  </li>
<li>\exercise{module=H3/algebra/oefpuis.fr&cmd=new&exo=quprin10 &cmd=new}{Une formule au hasard}  </li>
</ul>
</div>








</div></td><td valign=top halign=right> <div class="toc">\link{mainS2}


<font size=-2>
      \link{mainS2S1}{}</font>

<font size=-2>
      \link{mainS2S2}{}</font>

<font size=-2>
      \link{mainS2S3}{}</font>

<div class="selection"><font size=-2>
      \link{mainS2S4}{}</font></div>
</div><center>\reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width="20" height="20">}</center></tr></table>