Pertanyaan

5 ( p 2 1 × p 4 1 × p 6 1 × p 8 1 ) 8 = ...

$5 (p^{\frac{1}{2}} \times p^{\frac{1}{4}} \times p^{\frac{1}{6}} \times p^{\frac{1}{8}})^{8} = ...$

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Konsep yang digunakan: a m × a n ( a m ) n n a m = = = a m + n ( a ) m × n a n m Maka didapatkan: 5 ( p 2 1 × p 4 1 × p 6 1 × p 8 1 ) 8 = = = = = = = = 5 ( p 2 1 + 4 1 + 6 1 + 8 1 ) 8 5 ( p 24 12 + 6 + 4 + 3 ) 8 5 ( p 24 25 ) 8 5 ( p ) 24 25 × 8 5 p 3 25 p 5 3 25 p 3 25 5 × 5 1 p 3 5 Dengan demikian, 5 ( p 2 1 × p 4 1 × p 6 1 × p 8 1 ) 8 = p 3 5 . Jadi, jawaban yang tepat adalah C.

Konsep yang digunakan:

$a^{m} \times a^{n} (a^{m})^{n} n a^{m} = = = a^{m + n} (a)^{m \times n} a^{\frac{m}{n}}$

Maka didapatkan:

$5 (p^{\frac{1}{2}} \times p^{\frac{1}{4}} \times p^{\frac{1}{6}} \times p^{\frac{1}{8}})^{8} = = = = = = = = 5 (p^{\frac{1}{2} + \frac{1}{4} + \frac{1}{6} + \frac{1}{8}})^{8} 5 (p^{\frac{12 + 6 + 4 + 3}{24}})^{8} 5 (p^{\frac{25}{24}})^{8} 5 (p)^{\frac{25}{24} \times 8} 5 p^{\frac{25}{3}} p^{\frac{\frac{25}{3}}{5}} p^{\frac{25 5}{3} \times \frac{1}{5}} p^{\frac{5}{3}}$