Compute and simplify using scientific notation: evaluate (79 × 10^6) / (12 × 10^-8) and express the result in normalized form.

Introduction / Context:
Combining numbers in scientific notation streamlines calculations with very large or very small quantities. The key is to treat the numeric coefficients and the powers of ten separately, then normalize the final answer to standard scientific form (one nonzero digit before the decimal point).

Given Data / Assumptions:

• Expression: (79 × 10^6) / (12 × 10^-8).
• Rule: 10^a / 10^b = 10^(a − b).
• Normalization: keep coefficient between 1 and 10, adjusting the exponent accordingly.

Concept / Approach:

Divide coefficients and subtract exponents: (79 / 12) × 10^(6 − (−8)). Then, normalize the coefficient to have a single leading digit and adjust the exponent if needed. Rounding to three significant figures is typical unless specified otherwise.

Step-by-Step Solution:

Verification / Alternative check:

Approximation check: 80/10 = 8, close to 6.58; exact exponent remains 10^14, confirming the order of magnitude is correct.

Why Other Options Are Wrong:

6,580 × 10^12 = 6.58 × 10^15 (wrong exponent). 658 × 10^10 = 6.58 × 10^12 (too small). 0.658 × 10^16 = 6.58 × 10^15 (too large).

Common Pitfalls:

Adding instead of subtracting exponents in division; failing to normalize the coefficient; rounding excessively early.

Final Answer:

6.58 × 10^14