1. **State the problem:** Calculate $$\frac{2.5 \times 10^{8} \times 8.3 \times 10^{9}}{5.6 \times 10^{-3} - 9.7 \times 10^{-4}}$$ and express the answer in standard form to 2 significant figures. 2. **Calculate the numerator:** Multiply the coefficients and add the exponents of 10. $$2.5 \times 8.3 = 20.75$$ $$10^{8} \times 10^{9} = 10^{8+9} = 10^{17}$$ So numerator = $$20.75 \times 10^{17}$$ 3. **Calculate the denominator:** Subtract the two numbers. $$5.6 \times 10^{-3} - 9.7 \times 10^{-4} = 0.0056 - 0.00097 = 0.00463$$ 4. **Divide numerator by denominator:** $$\frac{20.75 \times 10^{17}}{0.00463} = 20.75 \times 10^{17} \times \frac{1}{0.00463}$$ Calculate $$\frac{1}{0.00463} \approx 215.92$$ So result = $$20.75 \times 215.92 \times 10^{17} = 4482.14 \times 10^{17}$$ 5. **Convert to standard form:** $$4482.14 \times 10^{17} = 4.48214 \times 10^{3} \times 10^{17} = 4.48214 \times 10^{20}$$ 6. **Round to 2 significant figures:** $$4.5 \times 10^{20}$$ **Final answer:** $$4.5 \times 10^{20}$$