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MATH / If r, s, and t are constants such that (x^(r−2)⋅y^(2s)⋅z^(3t+1))/(x^(2r)⋅y^(s−4)⋅z^(2t−3))=xyz for all non-zero x, y, and z, then solve for r^(s)⋅t. Express your answer as a fracti…

Problem

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problem

If rr, ss, and tt are constants such that xr−2⋅y2s⋅z3t+1x2r⋅ys−4⋅z2t−3=xyz\frac{x^{r-2}\cdot y^{2s}\cdot z^{3t+1}}{x^{2r}\cdot y^{s-4}\cdot z^{2t-3}}=xyz for all non-zero xx, yy, and zz, then solve for rs⋅tr^s\cdot t. Express your answer as a fraction.
Plain-text mathematical notation (without MathML)
If r, s, and t are constants such that (x^(r−2)⋅y^(2s)⋅z^(3t+1))/(x^(2r)⋅y^(s−4)⋅z^(2t−3))=xyz for all non-zero x, y, and z, then solve for r^(s)⋅t. Express your answer as a fraction.
Original LaTeX notation
If $r$, $s$, and $t$ are constants such that $\frac{x^{r-2}\cdot y^{2s}\cdot z^{3t+1}}{x^{2r}\cdot y^{s-4}\cdot z^{2t-3}}=xyz$ for all non-zero $x$, $y$, and $z$, then solve for $r^s\cdot t$. Express your answer as a fraction.

level

Level 5

type

Algebra

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Source and history

task_id
6fca7ca5-6685-56c1-8970-16ad7bb98818
task_key
algebra--test--6fca7ca5-6685-56c1-8970-16ad7bb98818
task_revision_id
1
config / split
algebra / test

Official source

initial import