Question: User: $(3 - x^2)\sqrt{(5x + 4)^3}$
1. **State the problem:** Simplify or analyze the expression $$ (3 - x^2) \sqrt{(5x + 4)^3} $$.
2. **Recall the properties of radicals and exponents:**
- The square root of a power can be rewritten using fractional exponents: $$ \sqrt{a^b} = a^{\frac{b}{2}} $$.
- Multiplying expressions involves distributing factors if needed.
3. **Rewrite the square root term:**
$$ \sqrt{(5x + 4)^3} = (5x + 4)^{\frac{3}{2}} $$.
4. **Rewrite the entire expression:**
$$ (3 - x^2)(5x + 4)^{\frac{3}{2}} $$.
5. **This is the simplified form using exponents.**
6. **If you want to expand or further simplify, note that expanding $(5x + 4)^{\frac{3}{2}}$ is complex and usually left as is unless specific values for $x$ are given.**
**Final simplified expression:**
$$ (3 - x^2)(5x + 4)^{\frac{3}{2}} $$