(1)) Simplify. Assume all variables are positive. \( \left(w^{5}\right)^{\frac{4}{3}} \) Write your answer in the form \( A \) or \( \frac{A}{R^{\prime}} \), where \( A \) and

To simplify the expression \( \left(w^{5}\right)^{\frac{4}{3}} \), follow these steps: 1. **Apply the Power of a Power Rule:** The rule states that \((a^{b})^{c} = a^{b \cdot c}\). Applying this to your expression: \[ \left(w^{5}\right)^{\frac{4}{3}} = w^{5 \cdot \frac{4}{3}} = w^{\frac{20}{3}} \] 2. **Express as a Mixed Exponent (Optional):** If you prefer to express the exponent as a whole number plus a fractional part: \[ w^{\frac{20}{3}} = w^{6 + \frac{2}{3}} = w^{6} \cdot w^{\frac{2}{3}} \] This can also be written using radicals: \[ w^{6} \cdot \sqrt[3]{w^{2}} \] 3. **Final Simplified Form:** The simplest form, using a single exponent, is: \[ w^{\frac{20}{3}} \] **Answer:** After simplifying, the expression is equal to \( w^{\,20/3} \).