Roboguru

Diketahui adalah senilai dengan . Dapatkan nilai .

Pertanyaan

Diketahui begin mathsize 14px style fraction numerator open parentheses x to the power of n minus 1 end exponent y to the power of n close parentheses cubed over denominator x to the power of 2 n end exponent y to the power of 6 plus n end exponent end fraction end style adalah senilai dengan begin mathsize 14px style x to the power of a y to the power of b end style. Dapatkan nilai begin mathsize 14px style b over a end style.

Pembahasan Soal:

ingat sifat bilangan berpangkat

begin mathsize 14px style 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 a to the power of n over a to the power of m equals a to the power of n minus m end exponent end style

, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses x to the power of n minus 1 end exponent y to the power of n close parentheses cubed over denominator x to the power of 2 n end exponent y to the power of 6 plus n end exponent end fraction end cell equals cell fraction numerator x to the power of 3 n minus 3 end exponent y to the power of 3 n end exponent over denominator x to the power of 2 n end exponent y to the power of 6 plus n end exponent end fraction end cell row blank equals cell x to the power of 3 n minus 3 minus 2 n end exponent y to the power of 3 n minus 6 minus n end exponent end cell row blank equals cell x to the power of n minus 3 end exponent y to the power of 2 n minus 6 end exponent end cell end table end style 

sehingga diperoleh begin mathsize 14px style a equals n minus 3 space dan space b equals 2 n minus 6 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight b over straight a end cell equals cell fraction numerator 2 straight n minus 6 over denominator straight n minus 3 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis straight n minus 3 right parenthesis over denominator straight n minus 3 end fraction end cell row blank equals 2 end table end style

Jadi, nilai begin mathsize 14px style b over a end style adalah 2.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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