Exponent rules with common base: Given 95^3.7 ÷ 95^0.9989 = 95^?, find the value of ? (choose the closest).

Introduction / Context:This is a direct application of the law of exponents for the same base: a^m / a^n = a^(m − n). The problem asks for the resulting exponent after division. Then select the closest value from the provided decimal options.

Given Data / Assumptions:

• Base = 95
• Exponents: 3.7 (numerator) and 0.9989 (denominator)

Concept / Approach:For equal-base division, subtract exponents. Therefore ? = 3.7 − 0.9989. Carry out the subtraction carefully to avoid decimal slips and compare with nearby choices (2.7, 2.99, etc.).

Step-by-Step Solution:

Verification / Alternative check:Compute back: 95^2.7 × 95^0.9989 = 95^(3.6989) ≈ 95^3.7 with a tiny deficit of 0.0011, confirming that 2.7 is the nearest rounded exponent among choices.

Why Other Options Are Wrong:

• 2.99, 3: much larger than 2.7011.
• 1.9, 2.4: smaller than 2.7011.

Common Pitfalls:Reversing the subtraction order (0.9989 − 3.7), or mistakenly adding exponents when dividing like bases.

Final Answer:2.7