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Hasil dari   adalah ...

Pertanyaan

Hasil dari  2 to the power of negative 2 end exponent plus 3 to the power of negative 3 end exponent plus 1 to the power of negative 4 end exponent adalah ...

Pembahasan Soal:

Ingat kembali sifat bilangan berpangkat negatif seperti berikut.

a to the power of negative m end exponent equals 1 over a to the power of m

Penyelesaiannya adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of negative 2 end exponent plus 3 to the power of negative 3 end exponent plus 1 to the power of negative 4 end exponent end cell equals cell 1 over 2 squared plus 1 over 3 cubed plus 1 over 1 to the power of 4 end cell row blank equals cell 1 fourth plus 1 over 27 plus 1 over 1 end cell row blank equals cell fraction numerator 27 plus 4 plus 108 over denominator 108 end fraction end cell row blank equals cell 139 over 108 end cell row blank equals cell 1 31 over 108 end cell end table


Dengan demikian, hasil dari 2 to the power of negative 2 end exponent plus 3 to the power of negative 3 end exponent plus 1 to the power of negative 4 end exponent adalah 1 31 over 108.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Rahma

Mahasiswa/Alumni Institut Teknologi Bandung

Terakhir diupdate 12 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

.

Pembahasan Soal:

Ingat bahwa undefined, undefined , undefined. Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 81 m to the power of x n to the power of x plus 2 y end exponent over denominator 3 m to the power of negative 3 y end exponent left parenthesis negative n to the power of x right parenthesis end fraction end cell equals cell fraction numerator 81 m to the power of x n to the power of x plus 2 y end exponent over denominator negative 3 m to the power of negative 3 y end exponent n to the power of x end fraction end cell row blank equals cell negative fraction numerator 81 m to the power of x n to the power of x plus 2 y end exponent over denominator 3 m to the power of negative 3 y end exponent n to the power of x end fraction end cell row blank equals cell negative 27 m to the power of x minus left parenthesis negative 3 y right parenthesis end exponent n to the power of x plus 2 y minus x end exponent end cell row blank equals cell negative 27 m to the power of x plus 3 y end exponent n to the power of 2 y end exponent end cell row blank equals cell negative 3 cubed m to the power of x plus 3 y end exponent n to the power of 2 y end exponent end cell end table end style

Jadi, jawaban yang tepat adalah A.
 

0

Roboguru

....

Pembahasan Soal:

Ingat bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of x times a to the power of y end cell equals cell a to the power of x plus y end exponent end cell row cell a to the power of x over a to the power of y end cell equals cell a to the power of x minus y end exponent end cell end table end style    

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 16 x to the power of negative 4 end exponent y squared z squared over denominator 64 x to the power of negative 2 end exponent y z to the power of negative 4 end exponent end fraction end cell equals cell fraction numerator up diagonal strike 16 to the power of 1 x squared y squared z squared z to the power of 4 over denominator up diagonal strike 64 to the power of 4 x to the power of 4 y end fraction end cell row blank equals cell fraction numerator x squared y squared z squared z to the power of 4 over denominator 4 x to the power of 4 y end fraction end cell row blank equals cell fraction numerator x to the power of 2 minus 4 end exponent y to the power of 2 minus 1 end exponent z to the power of 2 plus 4 end exponent over denominator 4 end fraction end cell row blank equals cell fraction numerator x to the power of negative 2 end exponent y to the power of 1 z to the power of 6 over denominator 4 end fraction end cell row blank equals cell fraction numerator y z to the power of 6 over denominator 4 x squared end fraction space space end cell end table end style          


Jadi, jawaban yang tepat adalah D.

0

Roboguru

.

Pembahasan Soal:

Ingat bahwa begin mathsize 14px style 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 end style, begin mathsize 14px style a to the power of negative n end exponent equals 1 over a to the power of n end style, dan begin mathsize 14px style 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 end style. Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 12 x to the power of negative 3 end exponent y over denominator negative 3 x cubed left parenthesis negative y right parenthesis to the power of negative 3 end exponent end fraction end cell equals cell negative fraction numerator 4 x to the power of negative 3 end exponent y left parenthesis negative y right parenthesis cubed right parenthesis over denominator x cubed end fraction end cell row blank equals cell negative 4 x to the power of negative 3 minus 3 end exponent y left parenthesis negative y cubed right parenthesis end cell row blank equals cell 4 x to the power of negative 3 minus 3 end exponent y left parenthesis y cubed right parenthesis end cell row blank equals cell 4 x to the power of negative 3 minus 3 end exponent y to the power of 1 plus 3 end exponent end cell row blank equals cell 4 x to the power of negative 6 end exponent y to the power of 4 end cell row blank equals cell fraction numerator 4 y to the power of 4 over denominator x to the power of 6 end fraction end cell end table end style

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Diketahui dan . Nilai dari  adalah ....

Pembahasan Soal:

Ingat bahwa undefined, begin mathsize 14px style a to the power of negative n end exponent equals 1 over a to the power of n end style, dan undefined.

Selanjutnya, perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p divided by q end cell equals cell fraction numerator x to the power of negative 2 end exponent y plus y to the power of negative 3 end exponent over denominator 3 x y end fraction divided by fraction numerator 13 x cubed over denominator y to the power of 4 end fraction space end cell row blank equals cell fraction numerator x to the power of negative 2 end exponent y plus y to the power of negative 3 end exponent over denominator 3 x y end fraction cross times fraction numerator y to the power of 4 over denominator 13 x cubed end fraction end cell row blank equals cell fraction numerator left parenthesis x to the power of negative 2 end exponent y plus y to the power of negative 3 end exponent right parenthesis y to the power of 4 over denominator 3 x y times 13 x cubed end fraction end cell row blank equals cell fraction numerator x to the power of negative 2 end exponent y to the power of 1 plus 4 end exponent plus y to the power of negative 3 plus 4 end exponent over denominator 39 x to the power of 1 plus 3 end exponent y end fraction end cell row blank equals cell fraction numerator x to the power of negative 2 end exponent y to the power of 5 plus y over denominator 39 x to the power of 4 y end fraction end cell row blank equals cell fraction numerator begin display style y to the power of 5 over x squared end style plus y over denominator 39 x to the power of 4 y end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator y to the power of 5 plus x squared y over denominator x squared end fraction end style over denominator 39 x to the power of 4 y end fraction end cell row blank equals cell fraction numerator y to the power of 5 plus x squared y over denominator x squared end fraction divided by fraction numerator 39 x to the power of 4 y over denominator 1 end fraction end cell row blank equals cell fraction numerator y to the power of 5 plus x squared y over denominator x squared end fraction cross times fraction numerator 1 over denominator 39 x to the power of 4 y end fraction end cell row blank equals cell fraction numerator y to the power of 5 plus x squared y over denominator 39 x to the power of 2 plus 4 end exponent y end fraction end cell row blank equals cell fraction numerator y to the power of 5 plus x squared y over denominator 39 x to the power of 6 y end fraction end cell end table end style

Jadi, jawaban yang tepat adalah B.

2

Roboguru

Sederhanakan setiap bentuk berikut ini !

Pembahasan Soal:

Sifat - Sifat Pangkat

1. a to the power of p times a to the power of q equals a to the power of p plus q end exponent  

2. a to the power of p over a to the power of q equals a to the power of p minus q end exponent 

3. a to the power of negative p end exponent equals 1 over a to the power of p

4. a to the power of 0 equals 1 

5. a to the power of 1 equals a 

Dengan menggunakan sifat - sifat di atas, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 24 a to the power of negative 2 end exponent b to the power of negative 2 end exponent c over denominator 6 a to the power of negative 2 end exponent b to the power of negative 3 end exponent c to the power of negative 6 end exponent end fraction end cell equals cell 24 over 6 times a to the power of negative 2 end exponent times a squared times b to the power of negative 2 end exponent times b cubed times c times c to the power of 6 end cell row blank equals cell 4 times a to the power of negative 2 plus 2 end exponent times b to the power of negative 2 plus 3 end exponent times c to the power of 1 plus 6 end exponent end cell row blank equals cell 4 times a to the power of 0 times b to the power of 1 times c to the power of 7 end cell row blank equals cell 4 times 1 times b times c to the power of 7 end cell row blank equals cell 4 b c to the power of 7 end cell end table 

Jadi, bentuk sederhana dari fraction numerator 24 a to the power of negative 2 end exponent b to the power of negative 2 end exponent c over denominator 6 a to the power of negative 2 end exponent b to the power of negative 3 end exponent c to the power of negative 6 end exponent end fraction adalah 4 b c to the power of 7.

4

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