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**Soroban** Hello, ZBomber

We must change the roots and powers into fractional exponents . . .

We have: .$\displaystyle \frac{x^{\frac{3}{5}}}{x^{\frac{4}{7}}} $

Then (as expected) subtract exponents: .$\displaystyle x^{\frac{3}{5}-\frac{4}{7}} \;=\;x^{\frac{21}{35} - \frac{20}{35}} \;=\;x^{\frac{1}{35}} $

We have: .$\displaystyle \left(x^{\frac{3}{4}}\cdot x^{\frac{5}{4}}\right)^{-2} \;=\;\left(x^{\frac{3}{4}+\frac{5}{4}}\right)^{-2} \;=\;\left(x^{\frac{8}{4}}\right)^{-2} \;=\;\left(x^2\right)^{-2} \;= \;x^{-4} \;=\;\frac{1}{x^4} $