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open parentheses negative x to the power of 9 y to the power of 7 divided by x cubed y to the power of 4 close parentheses divided by open square brackets x cubed y squared times open parentheses negative x squared y close parentheses close square brackets 

Pembahasan Video:

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis negative x to the power of 9 y to the power of 7 divided by x cubed y to the power of 4 right parenthesis divided by left square bracket x cubed y squared times open parentheses negative x squared y close parentheses right square bracket end cell equals cell fraction numerator negative x to the power of 9 y to the power of 7 divided by x cubed y to the power of 4 over denominator x cubed y squared times left parenthesis negative x squared y right parenthesis end fraction end cell row blank equals cell fraction numerator negative x to the power of open parentheses 9 minus 3 close parentheses end exponent y to the power of open parentheses 7 minus 4 close parentheses end exponent over denominator negative x to the power of open parentheses 3 plus 2 close parentheses end exponent y to the power of open parentheses 2 plus 1 close parentheses end exponent end fraction end cell row blank equals cell fraction numerator negative x to the power of 6 y cubed over denominator negative x to the power of 5 y cubed end fraction end cell row blank equals x end table 

 

Jadi, bentuk sederhana dari bentuk pengkat tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table.

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D. Entry

Terakhir diupdate 07 Juni 2021

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Sederhanakan perpangkatan berikut ini. c.

Pembahasan Soal:

Ingat kembali aturan-aturan bilangan berpangkat berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of m cross times a to the power of n end cell equals cell a to the power of m plus n end exponent end cell row cell a to the power of m over a to the power of n end cell equals cell a to the power of m minus n end exponent end cell row cell open parentheses a cross times b close parentheses to the power of m end cell equals cell a to the power of m cross times b to the power of m end cell row cell open parentheses a over b close parentheses to the power of m end cell equals cell a to the power of m over b to the power of m 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 end cell end table end style  

sehingga

  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 left parenthesis negative 2 comma 5 right parenthesis to the power of 4 cross times left parenthesis negative 2 comma 5 right parenthesis cubed end cell equals cell 2 squared cross times open parentheses negative 5 over 2 close parentheses to the power of 4 cross times open parentheses negative 5 over 2 close parentheses cubed end cell row blank equals cell 2 squared cross times open parentheses negative 5 over 2 close parentheses to the power of 4 plus 3 end exponent end cell row blank equals cell 2 squared cross times open parentheses negative 5 over 2 close parentheses to the power of 7 end cell row blank equals cell 2 squared cross times open parentheses negative 1 cross times 5 over 2 close parentheses to the power of 7 end cell row blank equals cell 2 squared cross times open parentheses negative 1 close parentheses to the power of 7 cross times open parentheses 5 over 2 close parentheses to the power of 7 end cell row blank equals cell negative 1 cross times 2 squared cross times 5 to the power of 7 over 2 to the power of 7 end cell row blank equals cell negative 1 cross times 2 squared over 2 to the power of 7 cross times 5 to the power of 7 end cell row blank equals cell negative 1 cross times 2 to the power of 2 minus 7 end exponent cross times 5 to the power of 7 end cell row blank equals cell negative 1 cross times 2 to the power of negative 5 end exponent cross times 5 to the power of 7 end cell row blank equals cell negative 5 to the power of 7 over 2 to the power of 5 end cell end table end style  

Jadi, bentuk sederhana dari undefined adalah begin mathsize 14px style negative 5 to the power of 7 over 2 to the power of 5 end style 

0

Roboguru

Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Perhatikan bahwa

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator a to the power of negative 2 end exponent b cubed c to the power of negative 1 end exponent over denominator a to the power of negative 1 end exponent b squared c cubed end fraction close parentheses squared end cell equals cell open parentheses a to the power of negative 2 minus left parenthesis negative 1 right parenthesis end exponent b to the power of 3 minus 2 end exponent c to the power of negative 1 minus 3 end exponent close parentheses squared end cell row blank equals cell open parentheses a to the power of negative 1 end exponent b to the power of 1 c to the power of negative 4 end exponent close parentheses squared end cell row blank equals cell a to the power of negative 1 cross times 2 end exponent b to the power of 1 cross times 2 end exponent c to the power of negative 4 cross times 2 end exponent end cell row blank equals cell a to the power of negative 2 end exponent b squared c to the power of negative 8 end exponent end cell row blank equals cell fraction numerator b squared over denominator a squared c to the power of 8 end fraction end cell end table

Jadi, bentuk sederhana dari open parentheses fraction numerator a to the power of negative 2 end exponent b cubed c to the power of negative 1 end exponent over denominator a to the power of negative 1 end exponent b squared c cubed end fraction close parentheses squared adalah fraction numerator b squared over denominator a squared c to the power of 8 end fraction 

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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

Tentukan hasil pemangkatan bilangan berpangkat berikut ! d. e. f.

Pembahasan Soal:

Ingatlah sifat-sifat bilangan berpangkat berikut.

left parenthesis straight i right parenthesis space open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m left parenthesis ii right parenthesis space 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 left parenthesis iii right parenthesis space open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent left parenthesis iv 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 open parentheses fraction numerator a to the power of 4 b to the power of 8 over denominator 16 d to the power of 4 x end exponent end fraction close parentheses to the power of 1 fourth end exponent end cell equals cell open parentheses a to the power of 4 b to the power of 8 close parentheses to the power of begin display style 1 fourth end style end exponent over open parentheses 16 d to the power of 4 x end exponent close parentheses to the power of begin display style 1 fourth end style end exponent end cell row blank equals cell fraction numerator open parentheses a to the power of 4 close parentheses to the power of begin display style 1 fourth end style end exponent times open parentheses b to the power of 8 close parentheses to the power of begin display style 1 fourth end style end exponent over denominator open parentheses 16 close parentheses to the power of begin display style 1 fourth end style end exponent times open parentheses d to the power of 4 x end exponent close parentheses to the power of begin display style 1 fourth end style end exponent end fraction end cell row blank equals cell fraction numerator a to the power of 4 cross times begin display style 1 fourth end style end exponent b to the power of 8 cross times begin display style 1 fourth end style end exponent over denominator 2 to the power of up diagonal strike 4 cross times begin display style fraction numerator 1 over denominator up diagonal strike 4 end fraction end style end exponent d to the power of up diagonal strike 4 x times begin display style fraction numerator 1 over denominator up diagonal strike 4 end fraction end style end exponent end fraction end cell row blank equals cell fraction numerator a b squared over denominator 2 d to the power of x end fraction end cell end table

e)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 27 a to the power of 6 over denominator 64 b to the power of 3 x end exponent end fraction close parentheses to the power of negative 1 third end exponent end cell equals cell open parentheses 27 a to the power of 6 close parentheses to the power of negative begin display style 1 third end style end exponent over open parentheses 64 b to the power of 3 x end exponent close parentheses to the power of negative begin display style 1 third end style end exponent end cell row blank equals cell fraction numerator open parentheses 3 cubed close parentheses to the power of negative begin display style 1 third end style end exponent times open parentheses a to the power of 6 close parentheses to the power of negative begin display style 1 third end style end exponent over denominator open parentheses 2 to the power of 6 close parentheses to the power of negative begin display style 1 third end style end exponent times open parentheses b to the power of 3 x end exponent close parentheses to the power of negative begin display style 1 third end style end exponent end fraction end cell row blank equals cell fraction numerator 3 to the power of negative 1 end exponent a to the power of negative 2 end exponent over denominator 2 to the power of negative 2 end exponent b to the power of negative x end exponent end fraction end cell row blank equals cell fraction numerator 2 squared b to the power of x over denominator 3 a squared end fraction end cell row blank equals cell fraction numerator 4 b to the power of x over denominator 3 a squared end fraction end cell end table

f)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative fraction numerator 8 a cubed b to the power of 6 over denominator 27 c to the power of 6 d to the power of 9 x end exponent end fraction close parentheses to the power of negative 2 over 3 end exponent end cell equals cell fraction numerator open parentheses negative 1 close parentheses to the power of negative begin display style 2 over 3 end style end exponent times open parentheses 8 a cubed b to the power of 6 close parentheses to the power of negative begin display style 2 over 3 end style end exponent over denominator open parentheses 27 c to the power of 6 d to the power of 9 x end exponent close parentheses to the power of negative begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator 1 times open parentheses 2 cubed close parentheses to the power of negative begin display style 2 over 3 end style end exponent times open parentheses a cubed close parentheses to the power of negative begin display style 2 over 3 end style end exponent times open parentheses b to the power of 6 close parentheses to the power of negative begin display style 2 over 3 end style end exponent over denominator open parentheses 3 cubed close parentheses to the power of negative begin display style 2 over 3 end style end exponent times open parentheses c to the power of 6 close parentheses to the power of negative begin display style 2 over 3 end style end exponent times open parentheses d to the power of 9 x end exponent close parentheses to the power of negative begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator 2 to the power of negative 2 end exponent a to the power of negative 2 end exponent b to the power of negative 4 end exponent over denominator 3 to the power of negative 2 end exponent c to the power of negative 4 end exponent d to the power of negative 6 x end exponent end fraction end cell row blank equals cell fraction numerator 3 squared c to the power of 4 d to the power of 6 x end exponent over denominator 2 squared a squared b to the power of 4 end fraction end cell row blank equals cell fraction numerator 9 c to the power of 4 d to the power of 6 x end exponent over denominator 4 a squared b to the power of 4 end fraction end cell end table

Dengan demikian, hasil pemangkatan dari  open parentheses fraction numerator a to the power of 4 b to the power of 8 over denominator 16 d to the power of 4 x end exponent end fraction close parentheses to the power of 1 fourth end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator a b squared over denominator 2 d to the power of x end fraction end cell end table , open parentheses fraction numerator 27 a to the power of 6 over denominator 64 b to the power of 3 x end exponent end fraction close parentheses to the power of negative 1 third end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 b to the power of x over denominator 3 a squared end fraction end cell end table, dan open parentheses negative fraction numerator 8 a cubed b to the power of 6 over denominator 27 c to the power of 6 d to the power of 9 x end exponent end fraction close parentheses to the power of negative 2 over 3 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 9 c to the power of 4 d to the power of 6 x end exponent over denominator 4 a squared b to the power of 4 end fraction end cell end table.

2

Roboguru

Pembahasan Soal:

Gunakan space sifat minus sifat space perpangkatan space berikut space colon  left parenthesis a to the power of p right parenthesis to the power of q equals a to the power of p q end exponent  a to the power of p over a to the power of q equals a to the power of p minus q end exponent  a to the power of negative p end exponent equals 1 over a to the power of p    S e d e r h a n a k a n space b e n t u k space p a n g k a t space h i n g g a space y a n g space p a l i n g space s e d e r h a n a space  fraction numerator 27 to the power of negative 1 end exponent a cubed b to the power of 6 over denominator 3 to the power of negative 3 end exponent a cubed b to the power of negative 6 end exponent end fraction equals fraction numerator left parenthesis 3 cubed right parenthesis to the power of negative 1 end exponent a cubed b to the power of 6 over denominator 3 to the power of negative 3 end exponent a cubed b to the power of negative 6 end exponent end fraction equals fraction numerator horizontal strike 3 to the power of negative 3 end exponent a cubed end strike b to the power of 6 over denominator horizontal strike 3 to the power of negative 3 end exponent a cubed end strike b to the power of negative 6 end exponent end fraction equals b to the power of 12

0

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