<h2>(a) Wärm dich etwas auf:</h2> <table class="table table-bordered table-striped"> <tr> <td>\( \frac{§§V5(-29,-20,1)§§}{§§V6(7,15,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V7(-29,-20,1)§§}{§§V8(7,15,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> <tr> <td>\( \frac{§§V10(4,10,1)§§}{§§V11(2,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V12(4,10,1)§§}{§§V13(2,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> <tr> <td>\( \frac{§§V15(-4,5,1)§§}{§§V16(3,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V17(-4,5,1)§§}{§§V18(3,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> <tr> <td>\( \frac{§§V20(32,40,5)§§}{§§V21(2,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V22(32,40,5)§§}{§§V23(2,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> <tr> <td>\( \frac{§§V25(71,80,1)§§}{§§V26(3,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V27(71,80,1)§§}{§§V28(3,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> <tr> <td>\( \frac{§§V30(43,50,1)§§}{§§V31(6,10,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V32(43,50,1)§§}{§§V33(6,10,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> <tr> <td>\( \frac{§§V35(12,15,1)§§}{§§V36(6,10,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V37(12,15,1)§§}{§§V38(6,10,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> </table> <img src="https://www.mathkiss.com/uploads/snake3.webp" width="100" /> <h2>Potenzgesetze (Merksätze):</h2> <table class="table"> <tr> <td>\( a^n \cdot a^m = a^{n+m} \)</td> <td>Produkt von Potenzen: Wenn die Basen gleich sind, werden die Exponenten addiert.</td> </tr> <tr> <td>\( \frac{a^n}{a^m} = a^{n-m} \)</td> <td>Quotient von Potenzen: Wenn die Basen gleich sind, werden die Exponenten subtrahiert.</td> </tr> <tr> <td>\( (a^n)^m = a^{n \cdot m} \)</td> <td>Potenz einer Potenz: Ein Exponent wird mit einem anderen multipliziert.</td> </tr> <tr> <td>\( a^n \cdot b^n = (a \cdot b)^n \)</td> <td>Produkt von ähnlichen Potenzen: Die Basen werden multipliziert und der Exponent bleibt gleich.</td> </tr> <tr> <td>\( \frac{a^n}{b^n} = \left(\frac{a}{b}\right)^n \)</td> <td>Quotient von ähnlichen Potenzen: Die Basen werden dividiert und der Exponent bleibt gleich.</td> </tr> </table> <h2>(b) Jetzt wird's etwas kniffliger:</h2> <table class="table table-bordered table-striped"> <tr> <td>\( \frac{§§V0(39,50,1)§§}{§§V1(8,15,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V2(39,50,1)§§}{§§V3(8,15,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> <!-- Ponovljeni zadaci iz (a) za dodatnu vježbu --> <tr> <td>\( \frac{§§V5(-29,-20,1)§§}{§§V6(7,15,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V7(-29,-20,1)§§}{§§V8(7,15,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> <tr> <td>\( \frac{§§V10(4,10,1)§§}{§§V11(2,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V12(4,10,1)§§}{§§V13(2,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> <tr> <td>\( \frac{§§V15(-4,5,1)§§}{§§V16(3,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> <td>\( \frac{§§V17(-4,5,1)§§}{§§V18(3,5,1)§§} = \large\square\large\square + \frac{\large\square}{\large\square} \)</td> </tr> </table>