Final answer:
The expression 4⁻³×3⁴×4² / 3⁵×4⁻² simplifies to 3/4 after applying the rules for exponents, specifically, adding and subtracting them based on their bases and then converting negative exponents into positive by taking the reciprocal.
Step-by-step explanation:
To simplify the expression 4⁻³×3⁴×4² / 3⁵×4⁻², we will apply the rules of exponents which allow us to add and subtract the powers when multiplying and dividing powers of the same base. First, let's separate the terms with the same base and simplify: For the base 4: 4⁻³×4² = 4(-3+2) = 4⁻¹, For the base 3: 3⁴ / 3⁵ = 3(4-5) = 3⁻¹. Now, we simplify the negative exponents by taking the reciprocal and converting them to positive exponents: 4⁻¹ = 1/4¹ = 1/4, 3⁻¹ = 1/3¹ = 1/3. For the remaining multiplication and division, we get (1/4) / (1/3) = (1/4) × (3/1) = 3/4. Thus, the simplified expression is 3/4, which corresponds to Option A.