If $\dfrac{x^{a} \cdot x^{b}}{x^{c}} = x^{2}$ and $a = 5,\ b = 4$, find $c$.

If $\dfrac{x^{a} \cdot x^{b}}{x^{c}} = x^{2}$ and $a = 5,\ b = 4$, find $c$.
  1. $5$
  2. $7$
  3. $11$
  4. $1$

Solution

Equate exponents: $a + b - c = 2$, so $5 + 4 - c = 2 \Rightarrow c = 7$.

Asked in: IMO

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