1. **State the problem:** Simplify the expression $$9p^{\frac{3}{4}}p^{\frac{2}{3}}$$ and write it as a single power and as a radical. 2. **Use the product rule for exponents:** When multiplying powers with the same base, add the exponents. 3. **Combine the powers of $p$:** $$p^{\frac{3}{4}} \times p^{\frac{2}{3}} = p^{\frac{3}{4} + \frac{2}{3}}$$ 4. **Find a common denominator for the exponents:** The denominators are 4 and 3, so the common denominator is 12. 5. **Convert the exponents:** $$\frac{3}{4} = \frac{9}{12}, \quad \frac{2}{3} = \frac{8}{12}$$ 6. **Add the exponents:** $$\frac{9}{12} + \frac{8}{12} = \frac{17}{12}$$ 7. **Rewrite the expression:** $$9p^{\frac{17}{12}}$$ 8. **Express 9 as a power:** $$9 = 3^2$$ 9. **Write the entire expression as a single power:** $$3^2 p^{\frac{17}{12}}$$ 10. **Write the expression as a radical:** Recall that $$p^{\frac{17}{12}} = \sqrt[12]{p^{17}}$$ So the expression is: $$3^2 \sqrt[12]{p^{17}}$$ **Final answers:** - As a single power: $$3^2 p^{\frac{17}{12}}$$ - As a radical: $$9 \sqrt[12]{p^{17}}$$