Pertanyaan

SBMPTN'15 TKPA 646/46 Diketahui a , b , x dan y adalah bilangan real positif. Jika a 3 ab 3 a 2 ab = a x b y , maka x − y adalah ....

SBMPTN'15 TKPA 646/46
Diketahui $a, b, x dan y$ adalah bilangan real positif. Jika $\frac{3 a ^{2} ab}{a 3 ab} = a^{x} b^{y}$ , maka $x - y$ adalah ....

$2$
$1$
$\frac{1}{2}$
$\frac{1}{3}$
$\frac{1}{6}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat kembali aturan perpangkatan berikut! ( ab ) m ( a m ) n a m ⋅ b n b n a m = = = = a m b n a mn a m + n a m − n Dengan aturan di atas, didapat perhitungan sebagai berikut. Dengan demikian, nilai dari x − y adalah 6 1 . Oleh karena itu, jawaban yang tepat adalah E.

Ingat kembali aturan perpangkatan berikut!

$(ab)^{m} (a^{m})^{n} a^{m} \cdot b^{n} \frac{a ^{m}}{b ^{n}} = = = = a^{m} b^{n} a^{mn} a^{m + n} a^{m - n}$

Dengan aturan di atas, didapat perhitungan sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cube root of a squared end root square root of a b end root over denominator square root of a cube root of a b end root end root end fraction end cell equals cell a to the power of x b to the power of y end cell row cell fraction numerator a to the power of begin display style 2 over 3 end style end exponent open parentheses a b close parentheses to the power of begin display style 1 half end style end exponent over denominator open parentheses a open parentheses a b close parentheses to the power of begin display style 1 third end style end exponent close parentheses to the power of begin display style 1 half end style end exponent end fraction end cell equals cell a to the power of x b to the power of y end cell row cell fraction numerator a to the power of begin display style 2 over 3 end style end exponent a to the power of begin display style 1 half end style end exponent b to the power of begin display style 1 half end style end exponent over denominator a to the power of begin display style 1 half end style end exponent a to the power of begin display style 1 over 6 end style end exponent b to the power of begin display style 1 over 6 end style end exponent end fraction end cell equals cell a to the power of x b to the power of y end cell row cell fraction numerator a to the power of begin display style 2 over 3 plus end style end exponent to the power of begin display style 1 half end style end exponent b to the power of begin display style 1 half end style end exponent over denominator a to the power of begin display style 1 half end style end exponent to the power of begin display style plus 1 over 6 end style end exponent b to the power of 1 over 6 end exponent end fraction end cell equals cell a to the power of x b to the power of y end cell row cell fraction numerator a to the power of begin display style 7 over 6 end style end exponent b to the power of begin display style 1 half end style end exponent over denominator a to the power of begin display style 2 over 3 end style end exponent b to the power of begin display style 1 over 6 end style end exponent end fraction end cell equals cell a to the power of x b to the power of y end cell row cell a to the power of 7 over 6 minus 2 over 3 end exponent times b to the power of 1 half minus 1 over 6 end exponent end cell equals cell a to the power of x b to the power of y end cell row cell a to the power of 1 half end exponent b to the power of 1 third end exponent end cell equals cell a to the power of x b to the power of y end cell row blank blank blank row x equals cell 1 half end cell row y equals cell 1 third end cell row blank blank blank row cell x minus y end cell equals cell 1 half minus 1 third end cell row blank equals cell fraction numerator 3 minus 2 over denominator 6 end fraction end cell row blank equals cell 1 over 6 end cell end table$

Dengan demikian, nilai dari $x - y$ adalah $\frac{1}{6}$ .