PRACTICE QUESTIONS COMPETITION WING

 If $(1331{)}^{-\mathrm{x}}=(225{)}^{\mathrm{y}}$, where $\mathrm{x}$ and $\mathrm{y}$ are integers, then find the value of $3\mathrm{xy}$.

 If $(\sqrt{3}{)}^{\mathrm{x}+\mathrm{y}}=9$ and $(\sqrt{2}{)}^{\mathrm{x}-\mathrm{y}}=32$, then $2\mathrm{x}+\mathrm{y}$ is _____.

 If $6^{\mathrm{x}-\mathrm{y}}=36$ and $3^{\mathrm{x}+\mathrm{y}}=729$, then find ${\mathrm{x}}^2-{\mathrm{y}}^2$.

If ${\mathrm{p}}^{{\mathrm{q}}^{\mathrm{r}}}=512$, then find the manimum possible value of $\left(\mathrm{p}\right), \left(\mathrm{q}\right), \left(\mathrm{r}\right)$, where $\mathrm{p}, \mathrm{q} \mathrm{and} \mathrm{r}$ are positive integers.

 If $2^{\mathrm{x}+\mathrm{y}}=128$ and $4^{\mathrm{x}-\mathrm{y}}=16$, then find $\frac{\mathrm{x}}{\mathrm{y}}$.

If $2^{\mathrm{x}}=3^{\mathrm{y}}=6^{\mathrm{z}}$, then $\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{y}}+\frac{1}{\mathrm{z}}=$_____.

Which of the following is the descending order of ${\left(343\right)}^3, {\left(2401\right)}^2$ and ${\left(49\right)}^5$?

If ${\mathrm{x}}^{\mathrm{y}}={\mathrm{y}}^{\mathrm{z}}={\mathrm{z}}^{\mathrm{x}}$, and $\mathrm{xz}={\mathrm{y}}^2$, then which of the following is correct?