Final answer:
The simplified algebraic expression of (-8a⁵b)/(4ab⁶) is -2a⁴b⁻⁵, which can also be written as -2a⁴/b⁵ when expressing 'b' with a positive exponent.
Step-by-step explanation:
To simplify the given algebraic expression (-8a⁵b)/(4ab⁶), we will need to perform algebraic operations which include dividing the coefficients and subtracting the powers for like bases.
First, we divide the coefficients (-8) by (4) which equals (-2). Next, we subtract the exponent of 'a' in the numerator from the exponent of 'a' in the denominator (5 - 1 = 4), and the exponent of 'b' in the numerator from the exponent of 'b' in the denominator (1 - 6 = -5). Always remember that when dividing powers with the same base, you subtract the exponents.
This results in the simplified expression -2a⁴b⁻⁵, which means -2 times 'a' to the fourth power times 'b' to the negative fifth power. The negative exponent indicates that 'b' is on the denominator when expressed as a positive exponent.
Lastly, to express 'b' with a positive exponent, the expression becomes -2a⁴/b⁵.