Pertanyaan

Sederhanakanlah .

Sederhanakanlah $begin mathsize 14px style open parentheses fraction numerator 2 p to the power of 5 q to the power of negative 3 end exponent r over denominator 4 p squared q squared r to the power of negative 2 end exponent end fraction close parentheses cubed end style$ .

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Jawaban terverifikasi

Jawaban

bentuk sederhana dari adalah .

bentuk sederhana dari $begin mathsize 14px style open parentheses fraction numerator 2 p to the power of 5 q to the power of negative 3 end exponent r over denominator 4 p squared q squared r to the power of negative 2 end exponent end fraction close parentheses cubed end style$ adalah $begin mathsize 14px style fraction numerator p to the power of 9 r to the power of 9 over denominator 8 q to the power of 15 end fraction end style$ .

Pembahasan

Dengan menggunakan sifat eksponen , maka didapatkan: . Jadi, bentuk sederhana dari adalah .

Dengan menggunakan sifat eksponen begin mathsize 14px style a to the power of n over a to the power of m equals a to the power of n minus m end exponent comma space open parentheses a to the power of n close parentheses to the power of m equals a to the power of n m end exponent comma space dan space a to the power of negative n end exponent equals 1 over a to the power of n end style , maka didapatkan:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 2 p to the power of 5 q to the power of negative 3 end exponent r over denominator 4 p squared q squared r to the power of negative 2 end exponent end fraction close parentheses cubed end cell equals cell fraction numerator 2 cubed p to the power of 15 q to the power of negative 9 end exponent r cubed over denominator 4 cubed p to the power of 6 q to the power of 6 r to the power of negative 6 end exponent end fraction end cell row blank equals cell fraction numerator 2 cubed p to the power of 15 q to the power of negative 9 end exponent r cubed over denominator open parentheses 2 squared close parentheses cubed p to the power of 6 q to the power of 6 r to the power of negative 6 end exponent end fraction end cell row blank equals cell fraction numerator 2 cubed p to the power of 15 q to the power of negative 9 end exponent r cubed over denominator 2 to the power of 6 p to the power of 6 q to the power of 6 r to the power of negative 6 end exponent end fraction end cell row blank equals cell 2 to the power of 3 minus 6 end exponent space p to the power of 15 minus 6 end exponent space q to the power of negative 9 minus 6 end exponent space r to the power of 3 minus open parentheses negative 6 close parentheses end exponent end cell row blank equals cell 2 to the power of negative 3 end exponent space p to the power of 9 space q to the power of negative 15 end exponent space r to the power of 9 end cell row blank equals cell fraction numerator p to the power of 9 r to the power of 9 over denominator 2 cubed q to the power of 15 end fraction end cell row blank equals cell fraction numerator p to the power of 9 r to the power of 9 over denominator 8 q to the power of 15 end fraction end cell end table end style$ .

Jadi, bentuk sederhana dari $begin mathsize 14px style open parentheses fraction numerator 2 p to the power of 5 q to the power of negative 3 end exponent r over denominator 4 p squared q squared r to the power of negative 2 end exponent end fraction close parentheses cubed end style$ adalah $begin mathsize 14px style fraction numerator p to the power of 9 r to the power of 9 over denominator 8 q to the power of 15 end fraction end style$ .