1. **State the problem:** Simplify the expression $$(x^x+3)(2x^4)$$. 2. **Recall the distributive property:** When multiplying a sum by a term, multiply each addend by the term: $$a(b+c) = ab + ac$$ 3. **Apply the distributive property:** $$(x^x+3)(2x^4) = (x^x)(2x^4) + 3(2x^4)$$ 4. **Simplify each term:** - For the first term, multiply coefficients and add exponents of like bases: $$ (x^x)(2x^4) = 2x^{x+4} $$ - For the second term: $$ 3(2x^4) = 6x^4 $$ 5. **Write the final simplified expression:** $$ 2x^{x+4} + 6x^4 $$ This is the simplified form of the original expression.