Bentuk sederhana (20x−1y5z25x3y−3z4)−21 adalah ...

Pertanyaan

Bentuk sederhana $\left(\frac{5x^3y^{-3}z^4}{20x^{-1}y^5z^2}\right)^{-\frac12}$ adalah ...

$fraction numerator y to the power of 4 over denominator 2 x squared z cubed end fraction$
$fraction numerator y to the power of 4 over denominator 2 x squared z end fraction$
$fraction numerator 2 y to the power of 4 over denominator x squared z end fraction$
$fraction numerator 2 x squared over denominator y to the power of 4 z cubed end fraction$
$fraction numerator 2 y to the power of 4 over denominator x squared z cubed end fraction$

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Ingat sifat bilangan berpangkat:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x y close parentheses to the power of n end cell equals cell x to the power of n y to the power of n end cell row cell open parentheses x to the power of m close parentheses to the power of n end cell equals cell x to the power of m n end exponent end cell row cell x to the power of m over x to the power of n end cell equals cell x to the power of m minus n end exponent end cell row cell x to the power of negative m end exponent end cell equals cell 1 over x to the power of m end cell end table$

maka

$\begin{array}{rcl}\left(\frac{5x^3y^{-3}z^4}{20x^{-1}y^5z^2}\right)^{-\frac12}&=&\left(\frac5{20}\cdot\frac{x^3}{x^{-1}}\cdot\frac{y^{-3}}{y^5}\cdot\frac{z^4}{z^2}\right)^{-\frac12}\\&=&\left(\frac5{20}\right)^{-\frac12}\cdot\left(\frac{x^3}{x^{-1}}\right)^{-\frac12}\cdot\left(\frac{y^{-3}}{y^5}\right)^{-\frac12}\cdot\left(\frac{z^4}{z^2}\right)^{-\frac12}\\&=&\left(\frac14\right)^{-\frac12}\cdot\left(\frac{x^{-{\displaystyle\frac32}}}{x^{\displaystyle\frac12}}\right)\cdot\left(\frac{y^{\displaystyle\frac32}}{y^{-{\displaystyle\frac52}}}\right)\cdot\left(\frac{z^{-{\displaystyle\frac42}}}{z^{-{\displaystyle\frac22}}}\right)\\&=&\left(\frac1{2^2}\right)^{-\frac12}\cdot\left(\frac{x^{-{\displaystyle\frac32}}}{x^{\displaystyle\frac12}}\right)\cdot\left(\frac{y^{\displaystyle\frac32}}{y^{-{\displaystyle\frac52}}}\right)\cdot\left(\frac{z^{-{\displaystyle\frac42}}}{z^{-{\displaystyle\frac22}}}\right)\\&=&2^{-2\left(-\frac12\right)}\cdot x^{4\left(-\frac12\right)}\cdot y^{-8\left(-\frac12\right)}\cdot z^{2\left(-\frac12\right)}\\&=&2^1\cdot x^{-2}\cdot y^4\cdot z^{-1}\\&=&2\cdot\frac1{x^2}\cdot y^4\cdot\frac1z\\&=&\frac{2y^4}{x^2z}\end{array}$

Bentuk sederhana $open parentheses fraction numerator 5 x cubed y to the power of negative 3 end exponent z to the power of 4 over denominator 20 x to the power of negative 1 end exponent y to the power of 5 z squared end fraction close parentheses to the power of negative 1 half end exponent$ adalah $fraction numerator 2 y to the power of 4 over denominator x squared z end fraction$ .

Oleh karena itu, jawaban yang benar adalah C.

Jawaban terverifikasi

Dijawab oleh:

N. Puspita

Terakhir diupdate 07 Oktober 2021