Tentukan hasil operasi bilangan berpangkat berikut! d. e. f. x3n−5÷x2n+7

Pertanyaan

Tentukan hasil operasi bilangan berpangkat berikut!

d. 2 to the power of 4 divided by open parentheses 2 to the power of negative 9 end exponent cross times 2 to the power of 5 close parentheses
e. a to the power of 6 b to the power of negative 4 end exponent divided by a to the power of negative 2 end exponent b to the power of 5
f. x to the power of 3 n minus 5 end exponent divided by x to the power of 2 n plus 7 end exponent

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

hasil dari  2 to the power of 4 divided by open parentheses 2 to the power of negative 9 end exponent cross times 2 to the power of 5 close parentheses equals 256, a to the power of 6 b to the power of negative 4 end exponent divided by a to the power of negative 2 end exponent b to the power of 5 equals a to the power of 8 over b to the power of 9, dan x to the power of 3 n minus 5 end exponent divided by x to the power of 2 n plus 7 end exponent equals x to the power of n minus 12 end exponent.

Pembahasan

Ingatlah sifat-sifat bilangan berpangkat berikut.

left parenthesis straight i right parenthesis space a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent left parenthesis ii right parenthesis space 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 left parenthesis iii right parenthesis space a to the power of negative m end exponent equals 1 over a to the power of m

Berdasarkan sifat-sifat di atas, maka:

d)

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of 4 divided by open parentheses 2 to the power of negative 9 end exponent cross times 2 to the power of 5 close parentheses end cell equals cell 2 to the power of 4 divided by 2 to the power of negative 9 plus 5 end exponent end cell row blank equals cell 2 to the power of 4 divided by 2 to the power of negative 4 end exponent end cell row blank equals cell 2 to the power of 4 minus open parentheses negative 4 close parentheses end exponent end cell row blank equals cell 2 to the power of 4 plus 4 end exponent end cell row blank equals cell 2 to the power of 8 end cell row blank equals 256 end table

e)

table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of 6 b to the power of negative 4 end exponent divided by a to the power of negative 2 end exponent b to the power of 5 end cell equals cell a to the power of 6 minus open parentheses negative 2 close parentheses end exponent b to the power of negative 4 minus 5 end exponent end cell row blank equals cell a to the power of 6 plus 2 end exponent b to the power of negative 9 end exponent end cell row blank equals cell a to the power of 9 b to the power of negative 9 end exponent end cell row blank equals cell a to the power of 8 over b to the power of 9 end cell end table 

f)

table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of 3 n minus 5 end exponent divided by x to the power of 2 n plus 7 end exponent end cell equals cell x to the power of left parenthesis 3 n minus 5 right parenthesis minus open parentheses 2 n plus 7 close parentheses end exponent end cell row blank equals cell x to the power of 3 n minus 5 minus 2 n minus 7 end exponent end cell row blank equals cell x to the power of n minus 12 end exponent end cell end table 

Dengan demikian, hasil dari  2 to the power of 4 divided by open parentheses 2 to the power of negative 9 end exponent cross times 2 to the power of 5 close parentheses equals 256, a to the power of 6 b to the power of negative 4 end exponent divided by a to the power of negative 2 end exponent b to the power of 5 equals a to the power of 8 over b to the power of 9, dan x to the power of 3 n minus 5 end exponent divided by x to the power of 2 n plus 7 end exponent equals x to the power of n minus 12 end exponent.

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