Scientific notation with powers of ten: Compute (24 × 10^11) ÷ (3 × 10^4) and express the result using a power of ten.

Introduction / Context:
Mastering operations with scientific notation streamlines calculations in electronics and physics, where quantities routinely span many orders of magnitude. The key is to separate numeric factors from powers of ten and apply exponent laws consistently, then normalize the mantissa if needed.

Given Data / Assumptions:

• Expression: (24 × 10^11) ÷ (3 × 10^4).
• All quantities are positive real numbers; standard exponent rules apply.
• We seek a properly formed scientific-notation answer.

Concept / Approach:

Divide coefficients separately from the powers of ten. For exponents, use 10^a / 10^b = 10^(a − b). After computing, ensure the mantissa lies between 1 and 10 (or optionally adjust to engineering notation if multiples of 3 are desired).

Step-by-Step Solution:

Verification / Alternative check:

Rewrite 24 × 10^11 as 2.4 × 10^12. Then (2.4 × 10^12) ÷ (3 × 10^4) = 0.8 × 10^8 = 8 × 10^7 after normalization, confirming the same value.

Why Other Options Are Wrong:

• 8 × 10^4 / 8 × 10^11 / 8 × 10^15: These exponents reflect incorrect subtraction of powers.
• 0.8 × 10^8: Numerically equal but not normalized scientific notation; standard form prefers 8 × 10^7.

Common Pitfalls:

• Adding exponents instead of subtracting when dividing.
• Forgetting to normalize the mantissa into the 1–10 range.

Final Answer:

8 × 10^7