1. **State the problem:** Calculate the quotient $$\frac{1.50 \times 10^{5}}{5.0 \times 10^{1}}$$ and express the answer in scientific notation. 2. **Recall the rule for dividing numbers in scientific notation:** $$\frac{a \times 10^{m}}{b \times 10^{n}} = \frac{a}{b} \times 10^{m-n}$$ 3. **Apply the rule:** $$\frac{1.50 \times 10^{5}}{5.0 \times 10^{1}} = \frac{1.50}{5.0} \times 10^{5-1}$$ 4. **Simplify the fraction:** $$\frac{1.50}{5.0} = \cancel{\frac{1.50}{5.0}} = 0.3$$ 5. **Combine the powers of ten:** $$10^{5-1} = 10^{4}$$ 6. **Multiply the simplified fraction by the power of ten:** $$0.3 \times 10^{4}$$ 7. **Convert to proper scientific notation:** Since scientific notation requires the coefficient to be between 1 and 10, rewrite 0.3 as $3.0 \times 10^{-1}$: $$0.3 \times 10^{4} = (3.0 \times 10^{-1}) \times 10^{4} = 3.0 \times 10^{(-1+4)} = 3.0 \times 10^{3}$$ **Final answer:** $$\boxed{3.0 \times 10^{3}}$$