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Sederhanakan bentuk-bentuk di bawah ini dengan menggunakan sifat-sifat bilangan pangkat! f. (−6u3v)4÷(2uv2)2

Pertanyaan

Sederhanakan bentuk-bentuk di bawah ini dengan menggunakan sifat-sifat bilangan pangkat!

f. open parentheses negative 6 u cubed v close parentheses to the power of 4 divided by open parentheses 2 u v squared close parentheses squared 

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

bentuk sederhana dari table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 6 u cubed v close parentheses to the power of 4 divided by open parentheses 2 u v squared close parentheses squared end cell equals cell 18 squared times u to the power of 10 end cell end table 

Pembahasan

Bilangan berpangkat bulat positif dapat didefinisikan sebagai berikut.

a to the power of n equals stack a cross times a cross times a cross times horizontal ellipsis cross times a with underbrace below table row blank cell space space space space space space space space end cell cell n space text faktor end text end cell end table

Ingat sifat bilangan berpangkat 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

open parentheses a b close parentheses to the power of m equals a to the power of m times b to the power of m

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

a to the power of 0 equals 1 comma space a not equal to 0

sehingga bentuk sederhana dari soal di atas, yaitu

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative 6 u cubed v close parentheses to the power of 4 divided by open parentheses 2 u v squared close parentheses squared end cell row blank equals cell open parentheses open parentheses negative 6 close parentheses to the power of 4 open parentheses u cubed close parentheses to the power of 4 open parentheses v close parentheses to the power of 4 close parentheses divided by open parentheses open parentheses 2 close parentheses squared open parentheses u close parentheses squared open parentheses v squared close parentheses squared close parentheses end cell row blank equals cell open parentheses open parentheses 2 cross times open parentheses negative 3 close parentheses close parentheses to the power of 4 times u to the power of 12 times v to the power of 4 close parentheses divided by open parentheses 2 squared times u squared times v to the power of 4 close parentheses end cell row blank equals cell open parentheses 2 to the power of 4 times open parentheses negative 3 close parentheses to the power of 4 times u to the power of 12 times v to the power of 4 close parentheses divided by open parentheses 2 squared times u squared times v to the power of 4 close parentheses end cell row blank equals cell 2 to the power of 4 minus 2 end exponent times open parentheses negative 3 close parentheses to the power of 4 times u to the power of 12 minus 2 end exponent times v to the power of 4 minus 4 end exponent end cell row blank equals cell 2 squared times 81 times u to the power of 10 times v to the power of 0 end cell row blank equals cell 2 squared times 3 to the power of 4 times u to the power of 10 times 1 end cell row blank equals cell open parentheses 2 cross times 3 squared close parentheses squared times u to the power of 10 end cell row blank equals cell 18 squared times u to the power of 10 end cell end table

Dengan demikian, bentuk sederhana dari table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 6 u cubed v close parentheses to the power of 4 divided by open parentheses 2 u v squared close parentheses squared end cell equals cell 18 squared times u to the power of 10 end cell end table 

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