1. **Problem:** Simplify $$\frac{\sqrt[4]{z^5}}{\sqrt[4]{z}}$$ using the Quotient of Powers Property. 2. **Formula:** The Quotient of Powers Property states $$\frac{a^m}{a^n} = a^{m-n}$$ for the same base $a$. 3. **Step-by-step:** - Rewrite the expression using rational exponents: $$\frac{z^{\frac{5}{4}}}{z^{\frac{1}{4}}}$$ - Apply the Quotient of Powers Property: $$z^{\frac{5}{4} - \frac{1}{4}}$$ - Simplify the exponent: $$z^{\frac{4}{4}} = z^1 = z$$ 4. **Answer:** $$z$$ 1. **Problem:** Simplify $$\frac{b^{\frac{3}{4}}}{\sqrt[4]{b^2}}$$. 2. **Formula:** Same as above. 3. **Step-by-step:** - Rewrite the denominator: $$\sqrt[4]{b^2} = b^{\frac{2}{4}} = b^{\frac{1}{2}}$$ - Expression becomes: $$\frac{b^{\frac{3}{4}}}{b^{\frac{1}{2}}}$$ - Apply Quotient of Powers: $$b^{\frac{3}{4} - \frac{1}{2}}$$ - Find common denominator: $$\frac{3}{4} - \frac{2}{4} = \frac{1}{4}$$ - Result: $$b^{\frac{1}{4}} = \sqrt[4]{b}$$ 4. **Answer:** $$\sqrt[4]{b}$$ 1. **Problem:** Simplify $$\frac{\sqrt{c^5}}{\sqrt[3]{c}}$$. 2. **Formula:** Same as above. 3. **Step-by-step:** - Rewrite with rational exponents: $$\frac{c^{\frac{5}{2}}}{c^{\frac{1}{3}}}$$ - Apply Quotient of Powers: $$c^{\frac{5}{2} - \frac{1}{3}}$$ - Find common denominator: $$\frac{15}{6} - \frac{2}{6} = \frac{13}{6}$$ - Result: $$c^{\frac{13}{6}}$$ 4. **Answer:** $$c^{\frac{13}{6}}$$