Tentukan hasil pemangkatan berikut! e. (−6y5x)3 f. (−5n3m)−5 g. (−5xy4m)−3 f. (−7xy2mn)−4

Pertanyaan

Tentukan hasil pemangkatan berikut!

e. $open parentheses negative fraction numerator 5 x over denominator 6 y end fraction close parentheses cubed$

f. $open parentheses negative fraction numerator 3 m over denominator 5 n end fraction close parentheses to the power of negative 5 end exponent$

g. $open parentheses negative fraction numerator 4 m over denominator 5 x y end fraction close parentheses to the power of negative 3 end exponent$

f. $open parentheses negative fraction numerator 2 m n over denominator 7 x y end fraction close parentheses to the power of negative 4 end exponent$

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Ingat kembali aturan eksponen untuk bilangan pecahan berpangkat berikut ini!

open parentheses a over b close parentheses to the power of n equals stack stack a over b cross times a over b cross times a over b cross times.... cross times a over b with underbrace below with n space f a k t o r below

dengan b not equal to 0 dan adalah bilangan bulat.

Serta aturan eksponen: a to the power of negative m end exponent equals 1 over a to the power of m

Ada 2 aturan perpangkatan pada bilangan negatif, diantaranya adalah:

Jika dipangkatkan dengan bilangan genap pasti hasilnya akan positif
Jika dipangkatkan dengan bilangan ganjil pasti hasilnya akan negatif

Dengan aturan eksponen di atas, diperoleh perhitungan sebagai berikut.

e. $open parentheses negative fraction numerator 5 x over denominator 6 y end fraction close parentheses cubed$ , maka hasil pemangkatannya:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative fraction numerator 5 x over denominator 6 y end fraction close parentheses cubed end cell equals cell open parentheses negative fraction numerator 5 x over denominator 6 y end fraction close parentheses cross times open parentheses negative fraction numerator 5 x over denominator 6 y end fraction close parentheses cross times open parentheses negative fraction numerator 5 x over denominator 6 y end fraction close parentheses end cell row blank equals cell negative fraction numerator 125 x cubed over denominator 216 y cubed end fraction end cell end table$

f. $open parentheses negative fraction numerator 3 m over denominator 5 n end fraction close parentheses to the power of negative 5 end exponent$ , maka hasil pemangkatannya:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative fraction numerator 3 m over denominator 5 n end fraction close parentheses to the power of negative 5 end exponent end cell equals cell 1 over open parentheses negative fraction numerator 3 m over denominator 5 n end fraction close parentheses to the power of 5 end cell row blank equals cell open parentheses negative fraction numerator 5 n over denominator 3 m end fraction close parentheses to the power of 5 end cell row blank equals cell open parentheses negative fraction numerator 5 n over denominator 3 m end fraction close parentheses cross times open parentheses negative fraction numerator 5 n over denominator 3 m end fraction close parentheses cross times open parentheses negative fraction numerator 5 n over denominator 3 m end fraction close parentheses cross times open parentheses negative fraction numerator 5 n over denominator 3 m end fraction close parentheses cross times open parentheses negative fraction numerator 5 n over denominator 3 m end fraction close parentheses end cell row blank equals cell negative fraction numerator 3.125 n to the power of 5 over denominator 243 m to the power of 5 end fraction end cell end table end style$

g. $open parentheses negative fraction numerator 4 m over denominator 5 x y end fraction close parentheses to the power of negative 3 end exponent$ , maka hasil pemangkatannya:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative fraction numerator 4 m over denominator 5 x y end fraction close parentheses to the power of negative 3 end exponent end cell equals cell 1 over open parentheses negative fraction numerator 4 m over denominator 5 x y end fraction close parentheses cubed end cell row blank equals cell open parentheses negative fraction numerator 5 x y over denominator 4 m end fraction close parentheses cubed end cell row blank equals cell open parentheses negative fraction numerator 5 x y over denominator 4 m end fraction close parentheses cross times open parentheses negative fraction numerator 5 x y over denominator 4 m end fraction close parentheses cross times open parentheses negative fraction numerator 5 x y over denominator 4 m end fraction close parentheses end cell row blank equals cell negative fraction numerator 125 x cubed y cubed over denominator 64 m cubed end fraction end cell end table$

f. $open parentheses negative fraction numerator 2 m n over denominator 7 x y end fraction close parentheses to the power of negative 4 end exponent$ , maka hasil pemangkatannya:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative fraction numerator 2 m n over denominator 7 x y end fraction close parentheses to the power of negative 4 end exponent end cell equals cell 1 over open parentheses negative fraction numerator 2 m n over denominator 7 x y end fraction close parentheses to the power of 4 end cell row blank equals cell open parentheses negative fraction numerator 7 x y over denominator 2 m n end fraction close parentheses to the power of 4 end cell row blank equals cell open parentheses negative fraction numerator 7 x y over denominator 2 m n end fraction close parentheses cross times open parentheses negative fraction numerator 7 x y over denominator 2 m n end fraction close parentheses cross times open parentheses negative fraction numerator 7 x y over denominator 2 m n end fraction close parentheses cross times open parentheses negative fraction numerator 7 x y over denominator 2 m n end fraction close parentheses end cell row blank equals cell fraction numerator 2.401 x to the power of 4 y to the power of 4 over denominator 16 m to the power of 4 n to the power of 4 end fraction end cell end table$

Jadi, hasil pemangkatan bilangan tersebut adalah

(e) $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 125 x cubed over denominator 216 y cubed end fraction end cell end table$ ; (f) $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3.125 n to the power of 5 over denominator 243 m to the power of 5 end fraction end cell end table$ ; (g) $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 125 x cubed y cubed over denominator 64 m cubed end fraction end cell end table$ ;

(h) $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2.401 x to the power of 4 y to the power of 4 over denominator 16 m to the power of 4 n to the power of 4 end fraction end cell end table$ .