Tentukan nilai berikut! d. ((5/7)-(3/5))^(-3)

<p>Jawaban : &nbsp;- 6.364/3.375<br><br>Ingat!</p><p>Konsep bilangan berpangkat :</p><p>a⁻ⁿ = 1/aⁿ</p><p>(a/b)ⁿ = aⁿ/bⁿ</p><p>aⁿ = a × a × ... × a (dengan n bilangan bulat positif dan a sebanyak jumlah n)</p><p>&nbsp;</p><p>Pembahsan</p><p>(5/7 - &nbsp;3/5)⁻<strong>³</strong> = (5/7)⁻<strong>³</strong> - (3/5)⁻<strong>³</strong></p><p>= (5⁻<strong>³</strong>/7⁻<strong>³</strong>) - (3⁻<strong>³</strong>/5⁻<strong>³</strong>)</p><p>= (7<strong>³</strong>/5<strong>³</strong>) - (5<strong>³</strong>/3<strong>³</strong>)<br>= [(7×7×7)/(5×5×5) - (5×5×5)/(3×3×3)</p><p>= 343/125 - 125/27<br><br>Karena penyebut berbeda maka samakan dengan KPK dari 125 dan 27 yaitu 3.375</p><p>&nbsp;</p><p>343/125 = (343 × 27)/(125×27)</p><p>= 9.261/3.375</p><p>&nbsp;</p><p>125/27 = (125 × 125)/125×27)</p><p>= 15.625/3.375</p><p>&nbsp;</p><p>Maka</p><p>343/125 - 125/27</p><p>= 9.261/3.375 - 15.625/3.375</p><p>= (9.261 - 15.625)/3.375</p><p>= - 6.364/3.375<br>&nbsp;</p><p>Jadi, nilai dari (5/7 - &nbsp;3/5)⁻<strong>³</strong> &nbsp;adalah &nbsp;- 6.364/3.375</p>