Final answer:
To simplify the expression, we apply the laws of exponents and combine like terms to arrive at 10/b^9.
Step-by-step explanation:
To simplify the expression (2a⁴b⁻¹)((5a⁻¹b⁴)/(b⁶))⁴, we can apply the laws of exponents. First, let's simplify the denominator by subtracting the exponents: (5a⁻¹b⁴)/(b⁶) = 5a⁻¹b⁻². Next, we can simplify the expression by multiplying the exponents and combining like terms: (2a⁴b⁻¹) * (5a⁻¹b⁻²)⁴ = 2a⁴ * 5a⁻⁴ * b⁻¹ * b⁻⁸ = 10a^(4-4) * b^(-1-8) = 10a^0 * b^(-9) = 10 * b^(-9) = 10/b⁹. Therefore, the simplified form of the expression is 10/b⁹.