Express with positive exponents only: $a^{-3} b^{2} c^{-1}$.

Express with positive exponents only: $a^{-3} b^{2} c^{-1}$.
  1. $\dfrac{b^{2}}{a^{3} c}$
  2. $\dfrac{a^{3}}{b^{2} c}$
  3. $\dfrac{c}{a^{3} b^{2}}$
  4. $\dfrac{1}{a^{3} b^{2} c}$

Solution

Move factors with negative exponents to the denominator (and flip signs): $a^{-3} c^{-1}$ go down, $b^{2}$ stays up. Result: $\dfrac{b^{2}}{a^{3} c}$.

Asked in: IMO

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