Bentuk sederhana dari (a−2b4c2)−2(2a−1b−3c−2)−3 adalah ....

Pertanyaan

Bentuk sederhana dari $\style{font-size:14px}{\frac{\left(2a^{-1}b^{-3}c^{-2}\right)^{-3}}{\left(a^{-2}b^4c^2\right)^{-2}}}$ adalah ....

$begin mathsize 14px style fraction numerator a b to the power of 17 over denominator 8 c to the power of 10 end fraction end style$
$begin mathsize 14px style fraction numerator a b to the power of 17 over denominator 8 c to the power of 10 end fraction end style$
$begin mathsize 14px style fraction numerator 6 a c to the power of 10 over denominator b to the power of 17 end fraction end style$
$begin mathsize 14px style fraction numerator 8 a to the power of 10 over denominator b to the power of 12 c squared end fraction end style$
$begin mathsize 14px style fraction numerator b to the power of 17 c to the power of 10 over denominator 8 a end fraction end style$

S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat!

$\begin{array}{rcl}a^m\times a^n&=&a^{m+n}\\\left(a^m\right)^n&=&a^{m\times n}\\a^{-n}&=&\frac1{a^n}\end{array}$

Sehingga,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 a to the power of negative 1 end exponent b to the power of negative 3 end exponent c to the power of negative 2 end exponent close parentheses to the power of negative 3 end exponent over open parentheses a to the power of negative 2 end exponent b to the power of 4 c squared close parentheses to the power of negative 2 end exponent end cell equals cell fraction numerator 2 to the power of negative 3 end exponent a cubed b to the power of 9 c to the power of 6 over denominator a to the power of 4 b to the power of negative 8 end exponent c to the power of negative 4 end exponent end fraction end cell row blank equals cell 2 to the power of negative 3 end exponent a to the power of 3 minus 4 end exponent b to the power of 9 minus left parenthesis negative 8 right parenthesis end exponent c to the power of 6 minus left parenthesis negative 4 right parenthesis end exponent end cell row blank equals cell 2 to the power of negative 3 end exponent a to the power of negative 1 end exponent b to the power of 17 c to the power of 10 end cell row blank equals cell fraction numerator b to the power of 17 c to the power of 10 over denominator 2 cubed a to the power of 1 end fraction end cell row blank equals cell fraction numerator b to the power of 17 c to the power of 10 over denominator 8 a end fraction end cell end table end style$

Oleh karena itu, jawaban yang tepat adalah E.