Final answer:
Substituting a = 3 and b = -2 into the expression (3a⁻² b⁶)/(2a⁻¹ b⁵)² and simplifying, yields a final result of 0.046875.
Step-by-step explanation:
When a = 3 and b = -2, the value of the expression (3a⁻² b⁶)/(2a⁻¹ b⁵)² can be calculated by substituting the values and simplifying the expression. Following the order of operations, we first address the exponents and division in the numerator and the square of the denominator.
First, convert the exponents of a and b to reflect their negative exponents indicating reciprocation, and then calculate the expression by simplifying:
- Replace a with 3 and b with -2 in the expression.
- Simplify the exponents: (3/3²)*(-2)⁶ for the numerator, and [(2/3¹)*(-2)⁵]² for the denominator.
- Calculate the numerator: 3/9 * 64 = 21.33 (We use 64 because (-2)⁶ = 64).
- Calculate the denominator: (2/3 * -32)² = (2/3 * 32)² = (64/3)² = 4096/9.
- Divide the numerator by the denominator: 21.33 / (4096/9) = 21.33 * (9/4096) = 0.046875.
Therefore, the final result is 0.046875.