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Pertanyaan

Sederhanakan dan hitunglah.

a. open parentheses 5 over x close parentheses to the power of negative 2 end exponent times open parentheses fraction numerator 25 over denominator 3 x end fraction close parentheses to the power of 7 divided by open parentheses fraction numerator 5 over denominator 2 x end fraction close parentheses to the power of negative 4 end exponent 

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Jika a bilangan real dan n bilangan bulat positif, maka pangkat n dari a ditulis a to the power of n didefinisikan sebagai berikut.

a to the power of n equals stack a times a times a times a times horizontal ellipsis times a times a with underbrace below space space space space space space space space space space space space text sebanyak end text space n

Ingat sifat-sifat bilangan berpangkat (eksponen) berikut.

a to the power of m divided by a to the power of n equals a to the power of m minus n end exponent comma space a not equal to 0

a to the power of m times a to the power of n equals a to the power of m plus n end exponent

open parentheses a to the power of m close parentheses to the power of n equals a to the power of m n end exponent

open parentheses a divided by b close parentheses to the power of m equals a to the power of m divided by b to the power of m comma space b not equal to 0

a to the power of negative m end exponent equals 1 over a to the power of m comma space a not equal to 0

Penyelesaian soal di atas adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 5 over x close parentheses to the power of negative 2 end exponent times open parentheses fraction numerator 25 over denominator 3 x end fraction close parentheses to the power of 7 divided by open parentheses fraction numerator 5 over denominator 2 x end fraction close parentheses to the power of negative 4 end exponent end cell equals cell 5 to the power of negative 2 end exponent over x to the power of negative 2 end exponent times 25 to the power of 7 over open parentheses 3 x close parentheses to the power of 7 divided by 5 to the power of negative 4 end exponent over open parentheses 2 x close parentheses to the power of negative 4 end exponent end cell row blank equals cell 5 to the power of negative 2 end exponent over x to the power of negative 2 end exponent times fraction numerator open parentheses 5 squared close parentheses to the power of 7 over denominator 3 to the power of 7 times x to the power of 7 end fraction divided by fraction numerator 5 to the power of negative 4 end exponent over denominator 2 to the power of negative 4 end exponent times x to the power of negative 4 end exponent end fraction end cell row blank equals cell 5 to the power of negative 2 end exponent over x to the power of negative 2 end exponent times fraction numerator 5 to the power of 14 over denominator 3 to the power of 7 times x to the power of 7 end fraction divided by fraction numerator 5 to the power of negative 4 end exponent over denominator 2 to the power of negative 4 end exponent times x to the power of negative 4 end exponent end fraction end cell row blank equals cell fraction numerator 5 to the power of negative 2 plus 14 end exponent over denominator x to the power of negative 2 plus 7 end exponent times 3 to the power of 7 end fraction divided by fraction numerator 5 to the power of negative 4 end exponent over denominator 2 to the power of negative 4 end exponent times x to the power of negative 4 end exponent end fraction end cell row blank equals cell fraction numerator 5 to the power of 12 over denominator x to the power of 5 times 3 to the power of 7 end fraction cross times fraction numerator 2 to the power of negative 4 end exponent times x to the power of negative 4 end exponent over denominator 5 to the power of negative 4 end exponent end fraction end cell row blank equals cell 5 to the power of 12 minus open parentheses negative 4 close parentheses end exponent times 2 to the power of negative 4 end exponent times x to the power of negative 4 minus 5 end exponent times 1 over 3 to the power of 7 end cell row blank equals cell 5 to the power of 16 times 1 over 2 to the power of 4 times x to the power of negative 9 end exponent times 1 over 3 to the power of 7 end cell row blank equals cell 5 to the power of 16 times 1 over 2 to the power of 4 times 1 over x to the power of 9 times 1 over 3 to the power of 7 end cell row blank equals cell fraction numerator 5 to the power of 16 over denominator 2 to the power of 4 times 3 to the power of 7 times x to the power of 9 end fraction end cell end table

Dengan demikian, bentuk sederhana dari table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 5 over x close parentheses to the power of negative 2 end exponent times open parentheses fraction numerator 25 over denominator 3 x end fraction close parentheses to the power of 7 divided by open parentheses fraction numerator 5 over denominator 2 x end fraction close parentheses to the power of negative 4 end exponent end cell equals cell fraction numerator 5 to the power of 16 over denominator 2 to the power of 4 times 3 to the power of 7 times x to the power of 9 end fraction end cell end table 

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