mtgrulesboi
contestada

If r, s, and t are constants such that [tex]\frac{x^{r-2}\cdot y^{2s}\cdot z^{3t+1}}{x^{2r}\cdot y^{s-4}\cdot z^{2t-3}}=xyz[/tex] for all non-zero x, y, and z, then solve for [tex]r^s\cdot t[/tex]. Express your answer as a fraction.

Respuesta :

konrad509

[tex] \displaystyle
\frac{x^{r-2}\cdot y^{2s}\cdot z^{3t+1}}{x^{2r}\cdot y^{s-4}\cdot z^{2t-3}}=xyz\\\\
x^{-r-2}y^{s+4} z^{t+4}=xyz\\\\
-r-2=1 \wedge s+4=1 \wedge t+4=1\\
r=-3\wedge s=-3 \wedge t=-3\\\\
r^s\cdot t=(-3)^{-3}\cdot(-3)=(-3)^{-2}=\dfrac{1}{9} [/tex]

Answer:

Step-by-step explanation:

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