Final answer:
To simplify the given expression, divide the coefficients and subtract the exponents of the variables with the same base. The simplified expression is 2a⁻⁹b⁻²c².
Step-by-step explanation:
To simplify the expression 8a⁻⁵b⁻²c⁹/(4a⁴c⁷), we can divide the coefficients and subtract the exponents of the variables with the same base. In this case, we have:
8/4 = 2
a⁻⁵/a⁴ = a⁻⁵⁻⁴ = a⁻⁹
b⁻² remains the same
c⁹/c⁷ = c⁹⁻⁷ = c²
Combining these results, the simplified expression is 2a⁻⁹b⁻²c².