1. **Stating the problem:** We need to simplify and solve the expression $(120x^{0.3}y^{0.12}z) + (200x^{0.25}y^{0.12}z) = 150000000$. 2. **Understanding the terms:** The expression contains two terms with variables raised to powers and multiplied by coefficients. 3. **Check if terms can be combined:** Since the powers of $x$ differ (0.3 and 0.25), and powers of $y$ and $z$ are the same, these terms are not like terms and cannot be directly combined. 4. **Rewrite the equation:** $$120x^{0.3}y^{0.12}z + 200x^{0.25}y^{0.12}z = 150000000$$ 5. **Factor common terms:** Common factors are $y^{0.12}z$, so: $$y^{0.12}z(120x^{0.3} + 200x^{0.25}) = 150000000$$ 6. **Isolate the expression:** $$120x^{0.3} + 200x^{0.25} = \frac{150000000}{y^{0.12}z}$$ 7. **Final form:** The equation is simplified to this form. To solve for $x$, $y$, or $z$, more information or values are needed. **Answer:** $$y^{0.12}z(120x^{0.3} + 200x^{0.25}) = 150000000$$