1. **State the problem:** We need to find the value of $r$ such that $$600000 \times 10^4 = 600 \times 10^r.$$ 2. **Rewrite the numbers in scientific notation:** $600000 = 6 \times 10^5$ because $600000 = 6 \times 100000 = 6 \times 10^5$. 3. **Substitute into the equation:** $$6 \times 10^5 \times 10^4 = 600 \times 10^r.$$ 4. **Simplify the left side using the rule $10^a \times 10^b = 10^{a+b}$:** $$6 \times 10^{5+4} = 600 \times 10^r$$ $$6 \times 10^9 = 600 \times 10^r.$$ 5. **Rewrite 600 as $6 \times 10^2$:** $$6 \times 10^9 = 6 \times 10^2 \times 10^r.$$ 6. **Simplify the right side:** $$6 \times 10^9 = 6 \times 10^{2+r}.$$ 7. **Divide both sides by 6 to isolate powers of 10:** $$\frac{6 \times 10^9}{\cancel{6}} = \frac{6 \times 10^{2+r}}{\cancel{6}}$$ $$10^9 = 10^{2+r}.$$ 8. **Since the bases are equal, set the exponents equal:** $$9 = 2 + r.$$ 9. **Solve for $r$:** $$r = 9 - 2 = 7.$$ **Final answer:** $r = 7$