$$ (2.4 \times 10^3) \div (8 \times 10^{-2}) = $$ $x$

Concept & Formula This question requires combining scientific notation arithmetic and exponent rules for division. $$ \frac{a \times 10^m}{b \times 10^n} = \left(\frac{a}{b}\right) \times 10^{m-n} $$ Step-by-Step Solution * Group the numerical coefficients and the base-10 powers separately: $$ \left(\frac{2.4}{8}\right) \times \left(\frac{10^3}{10^{-2}}\right) $$ * Divide the coefficients. Since $$ \frac{24}{8} = 3 $$, it follows that $$ \frac{2.4}{8} = 0.3 $$. * Subtract the exponent of the denominator from the numerator's exponent: $$ 3 - (-2) = 3 + 2 = 5 $$ * Combine them to form $$ 0.3 \times 10^5 $$. * Convert to standard scientific form by moving the decimal point one place to the right, which decreases the exponent by 1: $$ 0.3 \times 10^5 = 3 \times 10^4 $$ Exam Strategy & Shortcut Treat 2.4 as 24 and divide by 8 to immediately get 3. This tells you the coefficient is related to 3. Then, quickly calculate the power of 10: $$ 3 - (-2) = 5 $$. Since we shifted a decimal (0.3 instead of 3), $$ 10^5 $$ becomes $$ 10^4 $$. You can mentally verify the order of magnitude to lock in the correct option in under 15 seconds. Common Pitfall Students often mishandle the subtraction of a negative exponent, mistakenly calculating $$ 3 - 2 = 1 $$ instead of $$ 3 - (-2) = 5 $$. Always write out or mentally vocalize the double negative explicitly when dividing exponents with negative signs. Final Answer **Therefore, the correct answer is $$ 3 \times 10^4 $$.**