Simplified Expression:
((mn^3)^2) * (((2^-2)(m^-1)(n^3))^(-2))
1. Simplify each part separately:
- (mn^3)^2 becomes m^2n^6.
- (((2^-2)(m^-1)(n^3))^(-2)) becomes (2^2)(m^1)(n^3).
2. Apply the negative exponent rule:
- 2^-2 becomes 2^2.
- m^-1 becomes m^1.
- n^3 remains n^3.
3. Simplify the remaining exponents:
- 2^2 is 4.
- m^1 is m.
- n^3 remains n^3.
4. Multiply all the simplified terms together:
4 * m * n^3 * m^2 * n^6.
5. Combine like terms:
4m^3n^9.
So, the simplified expression is 4m^3n^9.
