(-5)³ × (1/15)² × (10/3)⁴ × (9/5)⁵

<p>Jawaban: -1.296</p><p>&nbsp;</p><p>Konsep:</p><p>* a^m ⋅ aⁿ = a^{m + n}</p><p>* a^-n = 1/aⁿ</p><p>* (a^m)ⁿ = a^{m × n}</p><p>* (a ∙ b)ⁿ = aⁿ ∙ bⁿ</p><p>* (a/b)ⁿ = aⁿ/bⁿ</p><p>* aⁿ = a × a × a × ..... × a ⇒ sebanyak n kali</p><p>&nbsp;</p><p>Pembahasan:</p><p>(-5)³ × (1/15)² × (10/3)⁴ × (9/5)⁵</p><p>= (-5)³ × (1/(3 × 5))² × ((2 × 5)/3)⁴ × (3²/5)⁵</p><p>= (-5)³ × (1²/(3 × 5)²) × ((2 × 5)⁴/3⁴) × ((3²)⁵/5⁵)</p><p>= (-5)³ × (1/(3² × 5²)) × ((2⁴ × 5⁴)/3⁴) × (3¹⁰/5⁵)</p><p>= (-5)³ × (3² × 5²)^-1 × ((2⁴ × 5⁴) × 3^-⁴) × (3¹⁰×5^-⁵)</p><p>= (-5)³ × 3^-² × 5^-² × 2⁴ × 5⁴ × 3^-⁴ × 3¹⁰×5^-⁵</p><p>= (-5)³ × 3^-²^{+ (-4) + 10}× 2⁴ × 5^{-2 + 4 + (-5)}</p><p>= (-5)³ × 3⁴× 2⁴ × 5^-3</p><p>= (-5)³ × 3⁴× 2⁴ × 1/5³</p><p>= ((-5) × (-5) × (-5)) × 3⁴× 2⁴ × 1/125</p><p>= ((-125)/125) × (3× 2)⁴</p><p>= -1 × (6)⁴</p><p>= -1 × 6 × 6 × 6 × 6</p><p>= -1.296</p><p>&nbsp;</p><p>Jadi, hasilnya adalah -1.296.</p>