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Pertanyaan

Jika x equals 5 dan y equals 2, hitunglah nilai dari fraction numerator open parentheses x to the power of 5 y to the power of negative 3 end exponent close parentheses squared over denominator x to the power of 7 y to the power of negative 2 end exponent end fraction.

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

 nilai dari fraction numerator open parentheses x to the power of 5 y to the power of negative 3 end exponent close parentheses squared over denominator x to the power of 7 y to the power of negative 2 end exponent end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 125 over 16 end cell end table.

Pembahasan

Ingat kembali sifat bilangan berpangkat berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of m close parentheses to the power of n end cell equals cell a to the power of m n end exponent end cell row cell a to the power of m divided by a to the power of n end cell equals cell a to the power of m minus n end exponent end cell row cell a to the power of negative m end exponent end cell equals cell 1 over a to the power of m comma space a not equal to 0 end cell end table

Sehingga, diperoleh perhitungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses x to the power of 5 y to the power of negative 3 end exponent close parentheses squared over denominator x to the power of 7 y to the power of negative 2 end exponent end fraction end cell equals cell fraction numerator x to the power of 5 times 2 end exponent y to the power of negative 3 times 2 end exponent over denominator x to the power of 7 y to the power of negative 2 end exponent end fraction end cell row blank equals cell fraction numerator x to the power of 10 y to the power of negative 6 end exponent over denominator x to the power of 7 y to the power of negative 2 end exponent end fraction end cell row blank equals cell x to the power of 10 minus 7 end exponent y to the power of negative 6 minus open parentheses negative 2 close parentheses end exponent end cell row blank equals cell x cubed y to the power of negative 4 end exponent end cell row blank equals cell x cubed over y to the power of 4 end cell end table

Kemudian substitusikan nilai x equals 5 dan y equals 2.

table attributes columnalign right center left columnspacing 0px end attributes row cell x cubed over y to the power of 4 end cell equals cell 5 cubed over 2 to the power of 4 end cell row blank equals cell 125 over 16 end cell end table

Jadi, nilai dari fraction numerator open parentheses x to the power of 5 y to the power of negative 3 end exponent close parentheses squared over denominator x to the power of 7 y to the power of negative 2 end exponent end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 125 over 16 end cell end table.

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