1. **State the problem:** Identify the like terms in the expression $$-3x^{3} + 2^{4} + x^{5} - x^{3} + x^{4} - 4x^{5} + 5x - 5x^{5}$$. 2. **Recall the definition of like terms:** Like terms have the same variable raised to the same power. 3. **List the terms:** - $$-3x^{3}$$ - $$2^{4}$$ (which is a constant) - $$x^{5}$$ - $$-x^{3}$$ - $$x^{4}$$ - $$-4x^{5}$$ - $$5x$$ - $$-5x^{5}$$ 4. **Group like terms:** - Terms with $$x^{5}$$: $$x^{5}, -4x^{5}, -5x^{5}$$ - Terms with $$x^{3}$$: $$-3x^{3}, -x^{3}$$ - Term with $$x^{4}$$: $$x^{4}$$ (no like terms) - Term with $$x$$: $$5x$$ (no like terms) - Constant term: $$2^{4}$$ (which equals $$16$$) 5. **Final like terms groups:** - $$x^{5}$$ terms: $$x^{5}, -4x^{5}, -5x^{5}$$ - $$x^{3}$$ terms: $$-3x^{3}, -x^{3}$$ - Single terms: $$x^{4}, 5x, 16$$ **Answer:** The like terms are: - $$x^{5}$$ terms: $$x^{5}, -4x^{5}, -5x^{5}$$ - $$x^{3}$$ terms: $$-3x^{3}, -x^{3}$$