Pertanyaan

Sederhanakan bilangan berikut dengan menggunakan pangkat negatif! e. ( 2 ab ) 3 4 a f. a 2 + b 5 a g. ( x + 3 ) 4 5 x h. ( 2 m 2 n ) 3 4 m 3 n

Sederhanakan bilangan berikut dengan menggunakan pangkat negatif!

e. $\frac{4 a}{( 2 ab ) ^{3}}$

f. $\frac{a}{a ^{2} + b ^{5}}$

g. $\frac{5 x}{( x + 3 ) ^{4}}$

h. $\frac{4 m ^{3} n}{( 2 m ^{2} n ) ^{3}}$

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Ingat kembali aturan eksponen berikut ini! Dengan aturan eksponen di atas, diperoleh perhitungan sebagai berikut. d. , jika dinyatakan dalam pangkat negatif: e. , jika dinyatakan dalam pangkat negatif: f. , jika dinyatakan dalam pangkat negatif: g. , jika dinyatakan dalam pangkat negatif: Jadi, bentukpangkat negatif dari bilangan tersebut adalah (d) ;(e) ; (f) ; (g)

Ingat kembali aturan eksponen berikut ini!

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

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

Dengan aturan eksponen di atas, diperoleh perhitungan sebagai berikut.

d. $fraction numerator 4 a over denominator open parentheses 2 a b close parentheses cubed end fraction$ , jika dinyatakan dalam pangkat negatif:

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

e. $fraction numerator a over denominator a squared plus b to the power of 5 end fraction$ , jika dinyatakan dalam pangkat negatif:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator a squared plus b to the power of 5 end fraction end cell equals cell a times fraction numerator 1 over denominator a squared plus b to the power of 5 end fraction end cell row blank equals cell 1 over a to the power of negative 1 end exponent times open parentheses a to the power of negative 2 end exponent plus b to the power of negative 5 end exponent close parentheses end cell row blank equals cell fraction numerator open parentheses a to the power of negative 2 end exponent plus b to the power of negative 5 end exponent close parentheses over denominator a to the power of negative 1 end exponent end fraction end cell end table$

f. $fraction numerator 5 x over denominator left parenthesis x plus 3 right parenthesis to the power of 4 end fraction$ , jika dinyatakan dalam pangkat negatif:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 x over denominator left parenthesis x plus 3 right parenthesis to the power of 4 end fraction end cell equals cell 5 x times 1 over left parenthesis x plus 3 right parenthesis to the power of 4 end cell row blank equals cell 5 over x to the power of negative 1 end exponent times left parenthesis x plus 3 right parenthesis to the power of negative 4 end exponent end cell row blank equals cell fraction numerator 5 left parenthesis x plus 3 right parenthesis to the power of negative 4 end exponent over denominator x to the power of negative 1 end exponent end fraction end cell end table$

g. $fraction numerator 4 m cubed n over denominator open parentheses 2 m squared n close parentheses cubed end fraction$ , jika dinyatakan dalam pangkat negatif:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 4 m cubed n over denominator open parentheses 2 m squared n close parentheses cubed end fraction end cell equals cell fraction numerator 2 squared m cubed n over denominator 2 cubed m to the power of 2 times 3 end exponent n cubed end fraction end cell row blank equals cell fraction numerator 2 squared m cubed n over denominator 2 cubed m to the power of 6 n cubed end fraction end cell row blank equals cell open parentheses 2 squared over 2 cubed close parentheses open parentheses m cubed over m to the power of 6 close parentheses open parentheses n over n cubed close parentheses end cell row blank equals cell open parentheses 2 to the power of 2 minus 3 end exponent close parentheses open parentheses m to the power of 3 minus 6 end exponent close parentheses open parentheses n to the power of 1 minus 3 end exponent close parentheses end cell row blank equals cell 2 to the power of negative 1 end exponent m to the power of negative 3 end exponent n to the power of negative 2 end exponent end cell end table$

Jadi, bentuk pangkat negatif dari bilangan tersebut adalah

(d) Error converting from MathML to accessible text. ; (e) $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses a to the power of negative 2 end exponent plus b to the power of negative 5 end exponent close parentheses over denominator a to the power of negative 1 end exponent end fraction end cell end table$ ; (f) $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 5 left parenthesis x plus 3 right parenthesis to the power of negative 4 end exponent over denominator x to the power of negative 1 end exponent end fraction end cell end table$ ;

(g) Error converting from MathML to accessible text.