1. **State the problem:** Simplify the expression $$\frac{k^6 p^3 t^5}{k r^2 t^4}$$ assuming no denominator equals zero. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule to each variable:** - For $k$: $$\frac{k^6}{k} = k^{6-1} = k^5$$ - For $p$: $p^3$ remains as is since it is only in the numerator. - For $t$: $$\frac{t^5}{t^4} = t^{5-4} = t^1 = t$$ - For $r$: $r^2$ remains in the denominator. 4. **Write the simplified expression:** $$\frac{k^5 p^3 t}{r^2}$$ 5. **Show intermediate cancellation:** $$\frac{\cancel{k}^6 p^3 t^5}{\cancel{k} r^2 t^4} = \frac{k^{6-1} p^3 t^{5-4}}{r^2} = \frac{k^5 p^3 t}{r^2}$$ **Final answer:** $$\frac{k^5 p^3 t}{r^2}$$