Combine exponents of the same base: Compute the missing exponent k in (16)^9 ÷ (16)^4 × (16)^3 = (16)^k.

Introduction / Context:When multiplying or dividing powers with the same base, exponents add or subtract respectively. This is a direct application of the indices laws that allows consolidation to a single power of the base 16.

Given Data / Assumptions:

• Expression: 16^9 ÷ 16^4 × 16^3 = 16^k.
• All operations are on the same base (16).

Concept / Approach:Use two rules: a^m ÷ a^n = a^(m − n) and a^m × a^n = a^(m + n). Apply them in sequence to combine all powers into a single exponent k.

Step-by-Step Solution:

Verification / Alternative check:Rearranging the order (multiplication before division) still yields 9 − 4 + 3 = 8, confirming consistency.

Why Other Options Are Wrong:

• 10, 12: Result from adding all exponents or forgetting to subtract for division.
• 6.75, 7: Non-integer exponents not supported by the given integer-exponent operations.

Common Pitfalls:Applying multiplication and division in the wrong way to the exponents. Keep track: divide ⇒ subtract; multiply ⇒ add.

Final Answer:8