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Sederhanakan perpangkatan berikut ini. i. 253×83106×42​

Pertanyaan

Sederhanakan perpangkatan berikut ini.

i. begin mathsize 14px style fraction numerator 10 to the power of 6 cross times 4 squared over denominator 25 cubed cross times 8 cubed end fraction end style 

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

hasil sederhana dari fraction numerator 10 to the power of 6 cross times 4 squared over denominator 25 cubed cross times 8 cubed end fraction adalah 2.

Pembahasan

Ingat sifat-sifat bilangan berpangkat pada perkalian, pembagian, dan bilangan berpangkat dengan pangkat nol seperti berikut ini:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of 0 end cell equals 1 row cell open parentheses a to the power of p close parentheses to the power of n end cell equals cell a to the power of p cross times n end exponent end cell row cell open parentheses a cross times b close parentheses to the power of n end cell equals cell a to the power of n cross times b to the power of n end cell row cell a to the power of p cross times a to the power of q end cell equals cell a to the power of p plus q end exponent end cell row cell a to the power of p over a to the power of q end cell equals cell a to the power of p minus q end exponent end cell end table end style     

Selain itu rubahlah ke bilangan pokok 2 dan 3, sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 10 to the power of 6 cross times 4 squared over denominator 25 cubed cross times 8 cubed end fraction end cell equals cell fraction numerator open parentheses 5 cross times 2 close parentheses to the power of 6 cross times open parentheses 2 squared close parentheses squared over denominator open parentheses 5 squared close parentheses cubed cross times open parentheses 2 cubed close parentheses cubed end fraction end cell row blank equals cell fraction numerator 5 to the power of 6 cross times 2 to the power of 6 cross times 2 to the power of 4 over denominator 5 to the power of 6 cross times 2 to the power of 9 end fraction end cell row blank equals cell fraction numerator 5 to the power of 6 cross times 2 to the power of 6 plus 4 end exponent over denominator 5 to the power of 6 cross times 2 to the power of 9 end fraction end cell row blank equals cell fraction numerator 5 to the power of 6 cross times 2 to the power of 10 over denominator 5 to the power of 6 cross times 2 to the power of 9 end fraction end cell row blank equals cell 5 to the power of 6 minus 6 end exponent cross times 2 to the power of 10 minus 9 end exponent end cell row blank equals cell 5 to the power of 0 cross times 2 to the power of 1 end cell row blank equals cell 1 cross times 2 end cell row blank equals 2 end table end style   

Jadi, hasil sederhana dari fraction numerator 10 to the power of 6 cross times 4 squared over denominator 25 cubed cross times 8 cubed end fraction adalah 2.

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