We have supplied a reason for each of the remaining steps to the right of the corresponding result.
| `(du)/(dt)` | `=(pt^(p-1))/(qu^(q-1))` | |
| `=p/q(t^(p-1))/(u^(q-1))` | This is a rule for multiplication of quotients. | |
| `=p/q(t^(p-1))/((t^(p//q))^(q-1))` | We substituted for `u.` | |
| `=p/q (t^(p-1))/(t^((q-1)p//q))` | A power `x^n` itself raised to the power `m` is `x^(mn).` | |
| `=p/q(t^(p-1))/(t^(p-p//q))` | We carried out the multiplication in the exponent. | |
| `=p/qt^(p-1-p+p//q)` | We used properties of exponents | |
| `=p/qt^(-1+p//q)` | We cancelled `p` and `-p.` | |
| `=rt^(r-1)` | We substituted `r=ptext[/]q.` |