Jika diketahui x + y = 3, maka nilai dari [{9^(x-2y)} . {2^(2x-y+2)}] / [{3^(x-5y)} . {2^(x-2y+1)}].... Question from @gwenlauren36

izharulhaq78 $\displaystyle \frac{9^{\displaystyle x-2y}\times2^{\displaystyle 2x-y+2}}{3^{\displaystyle x-5y}\times2^{\displaystyle x-2y+1}}=\frac{(3^{\displaystyle 2})^{\displaystyle x-2y}\times2^{\displaystyle 2x-y+2}}{3^{\displaystyle x-5y}\times2^{\displaystyle x-2y+1}}\\\frac{9^{\displaystyle x-2y}\times2^{\displaystyle 2x-y+2}}{3^{\displaystyle x-5y}\times2^{\displaystyle x-2y+1}}=3^{\displaystyle 2x-4y-(x-5y)}2^{\displaystyle 2x-y+2-(x-2y+1)}$
$\displaystyle \frac{9^{\displaystyle x-2y}\times2^{\displaystyle 2x-y+2}}{3^{\displaystyle x-5y}\times2^{\displaystyle x-2y+1}}=3^{\displaystyle 2x-4y-x+5y}2^{\displaystyle 2x-y+2-x+2y-1}\\\frac{9^{\displaystyle x-2y}\times2^{\displaystyle 2x-y+2}}{3^{\displaystyle x-5y}\times2^{\displaystyle x-2y+1}}=3^{\displaystyle x+y}\times2^{\displaystyle x+y+1}$
$\displaystyle \frac{9^{\displaystyle x-2y}\times2^{\displaystyle 2x-y+2}}{3^{\displaystyle x-5y}\times2^{\displaystyle x-2y+1}}=3^{\displaystyle 3}\times2^{\displaystyle 3+1}\\\frac{9^{\displaystyle x-2y}\times2^{\displaystyle 2x-y+2}}{3^{\displaystyle x-5y}\times2^{\displaystyle x-2y+1}}=27\times2^{\displaystyle 4}\\\frac{9^{\displaystyle x-2y}\times2^{\displaystyle 2x-y+2}}{3^{\displaystyle x-5y}\times2^{\displaystyle x-2y+1}}=27\times16$
$\displaystyle \boxed{\boxed{\frac{9^{\displaystyle x-2y}\times2^{\displaystyle 2x-y+2}}{3^{\displaystyle x-5y}\times2^{\displaystyle x-2y+1}}=432}}$

1 votes Thanks 1

MicoArrafi $$\begin{align} \frac{9^{x-2y}\times2^{2x-y+2}}{3^{x-5y}\times2^{x-2y+1}}&=\frac{3^{2(x-2y)}\times2^{2x-y+2}}{3^{x-5y}\times2^{x-2y+1}}\\&=\frac{3^{2x-4y}\times2^{2x-y+2}}{3^{x-5y}\times2^{x-2y+1}}\\&=3^{(2x-4y)-(x-5y)}\times2^{(2x-y+2)-(x-2y+1)}\\&=3^{x+y}\times2^{x+y+1}\\&=3^3\times2^{3+1}\\&=3^3\times2^4\\&=27\times16\\&=\boxed{432} \end$

2 votes Thanks 2

Bantuin yg nomor 11 dan 12 dongg pleasee makasi banyakk

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Bantuin yg nomor 18 dong, beneran gak ngertii, makasii x gbu❤

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