(1)) Simplify. Assume all variables are positive.

Write your answer in the form or , where and

Ask by Zimmerman Harmon. in the United States

Jan 23,2025

Question

(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

UpStudy AI · Accepted Answer

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 $$ w^{\,20/3} $$.
$$ w^{\frac{20}{3}} $$

(1)) Simplify. Assume all variables are positive.

Write your answer in the form or , where and

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(1)) Simplify. Assume all variables are positive. Write your answer in the form or , where and