Final answer:
To simplify the given expression (2a³b⁻³)/(2⁻¹a⁻³b⁵), divide the coefficients and subtract the exponents of the variables with the same base. The simplified expression is 4a⁶b⁻⁸.
Step-by-step explanation:
To simplify the expression, we must use the laws of exponents. Specifically, we need to divide the terms and subtract the exponents. When we divide coefficients with the same base, we subtract the exponents, and when dividing numbers, we directly divide them.
The original expression provided is (2a³b⁻³)/(2⁻¹a⁻³b⁵). Let's break this down step by step:
- Divide the coefficients (numbers in front of the variables), which in this case are 2 and 2⁻¹. When you divide these, you simply get 2 divided by 1/2, which equals 4.
- For the variables with exponents, a³ divided by a⁻³, subtract the exponents (3 - (-3)) to get a⁶.
- For b⁻³ divided by b⁵, subtract the exponents (-3 - 5) to get b⁻⁸.
Combining all these results gives us the simplified form of the expression: 4a⁶b⁻⁸.