Final answer:
To simplify the expression (x²)⁻³(x⁻²) / (x²)⁻⁴, divide the two expressions with the same base and subtract the exponents. Simplify the bases to get the final answer of 1/x⁸.
Step-by-step explanation:
To simplify the expression (x²)⁻³(x⁻²) / (x²)⁻⁴, we can use the rule that states when we divide two numbers with the same base, subtract the exponents. In this case, we subtract -3 from -4, which gives us a final exponent of 1. Now, let's simplify the bases. (x²)⁻³ is equal to 1/x⁶, and (x⁻²) is equal to 1/x². Therefore, the expression simplifies to (1/x⁶)(1/x²) / 1/x² = 1/x⁸. So, the simplified expression is 1/x⁸.